Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and ...Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.展开更多
In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm ...In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.展开更多
It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1...It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.展开更多
In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the p...In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.展开更多
1 Main ResultWe consider a kind of multi-pseudo-differential operators, which is introduced by R. Coifman and Y.Meyer [1].Let symbol function σ（x , a, ε）∈C<sup>∞</sup>(R<sup>n</sup>×...1 Main ResultWe consider a kind of multi-pseudo-differential operators, which is introduced by R. Coifman and Y.Meyer [1].Let symbol function σ（x , a, ε）∈C<sup>∞</sup>(R<sup>n</sup>×R<sup>nm</sup>×R<sup>n</sup>) satisfy the following conditions:where x∈R<sup>n</sup>, a = （a<sub>1</sub>,…,a<sub>m</sub>） a-j∈R<sup>n</sup>,ζ∈R<sup>n</sup>, q = （q<sub>1</sub>,…,q<sub>m</sub>）, q<sub>j</sub>∈（Z+）<sup>n</sup> and q =|q<sub>1</sub>|+…+|q<sub>m</sub>|,The multi-pseudo-differential operator with the symbol o（x,α,ζ） is defined as展开更多
In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-dif...In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.展开更多
Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis ...Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis introduced.Later product and commutators for the PDO are investigated and their boundedness results are discussed.展开更多
In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to esta...In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.展开更多
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the author...In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained.展开更多
New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model arei...New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic ...This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.展开更多
Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. ...Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R（（x-1; 5）） is Baer （resp., quasi-Baer, PP, right zip） if and only if R is a Baer （resp., quasi-Baer, PP, right zip） ring. For a 5-weakly rigid ring R, R（（x-1;5）） is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.展开更多
Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new f...Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.展开更多
The purpose of this paper is to define a new symbol classand discuss the theory of two different pseudo-differential operators(p.d.o.)involving Fourier–Jacobi transform associated with a single symbol in.We also deri...The purpose of this paper is to define a new symbol classand discuss the theory of two different pseudo-differential operators(p.d.o.)involving Fourier–Jacobi transform associated with a single symbol in.We also derive boundedness results for p.d.o.’s in Sobolev type space.Anewpseudo-differential operator is developed using the product of symbols.Finally,norm inequality for commutators between two pseudo-differential operators is obtained.展开更多
In this paper,the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the fractional and pseudo-differential operators is obtained.
In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and stra...Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.展开更多
基金Supported by the National Natural Science Foundation of China(11871436,12071437)。
文摘Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.
文摘In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.
基金National Natural Science Foundation of China under Grant Nos.10371070 and 10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers,the Youth Foundation of Shanghai Education Committee,and Magnolia Grant of Shanghai Sciences and Technology Committee
文摘Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.
基金supported by the National Science Foundation of China NSFC(11161044,11131005)
文摘It is well known that the commutator Tb of the Calderbn-Zygmund singular integral operator is bounded on LP（Rn） for 1 〈 p 〈 ＋∞ if and only if b E BMO [1]. On the other hand, the commutator Tb is bounded from H1（Rn） into L1（Rn） only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσ be the operators that its symbol is Sσ1,δ with 0 ≤δ〈 1, if b ∈ LMO∞, then, the commutator [b, Tσ] is bounded from H1（Rn） into L1（Rn） and from L∞（Rn） into BMO（Rn）; If [b,Tσ] is bounded from H1（Rn） into L1（Rn） or L1（Rn） into BMO（Rn）, then, b ∈ LMOtoc.
基金The project supported by National Natural Science Foundation of China under Grant No.10401021
文摘In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given.
文摘1 Main ResultWe consider a kind of multi-pseudo-differential operators, which is introduced by R. Coifman and Y.Meyer [1].Let symbol function σ（x , a, ε）∈C<sup>∞</sup>(R<sup>n</sup>×R<sup>nm</sup>×R<sup>n</sup>) satisfy the following conditions:where x∈R<sup>n</sup>, a = （a<sub>1</sub>,…,a<sub>m</sub>） a-j∈R<sup>n</sup>,ζ∈R<sup>n</sup>, q = （q<sub>1</sub>,…,q<sub>m</sub>）, q<sub>j</sub>∈（Z+）<sup>n</sup> and q =|q<sub>1</sub>|+…+|q<sub>m</sub>|,The multi-pseudo-differential operator with the symbol o（x,α,ζ） is defined as
基金Supported by SERB MATRICS(Grant No.MTR2021/000266)。
文摘In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.
基金supported by Science and Engineering Research Board,Government of India,under Grant No.EMR/2016/005141。
文摘Pseudo-differential operators(PDO)Q(x,L_(a,x))and Q(x,L_(a,x))involving the index Whittaker transform are defined.Estimates for these operators in Hilbert space L_(2)^(a)(R+;m_(a)(x)dx)are obtained.A symbol classΩis introduced.Later product and commutators for the PDO are investigated and their boundedness results are discussed.
基金the National Natural Science Foundation of China (Grant No. 10571014)the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No. 20040027001)
文摘In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.
基金supported by National Natural Science Foundation of China(Grant No.10861010)
文摘In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.
基金Supported by National Natural Science Foundation of China (Grant No. 10871024)
文摘In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained.
基金Lucian Blaga University of Sibiu&Hasso Plattner Foundation Research Grants LBUS-IRG-2020-06.
文摘New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
基金supported by CSIR,New Delhi(Grant No.25(240)/15/EMR-Ⅱ)
文摘This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.
文摘Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R（（x-1; 5）） is Baer （resp., quasi-Baer, PP, right zip） if and only if R is a Baer （resp., quasi-Baer, PP, right zip） ring. For a 5-weakly rigid ring R, R（（x-1;5）） is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.
基金supported by the NSFC(11971475)the Natural Science Foundation of Jiangsu Province(BK20230708)+2 种基金the Natural Science Foundation for the Universities in Jiangsu Province(23KJB110003)Geng's research was supported by the NSFC(11201041)the China Postdoctoral Science Foundation(2019M651765)。
文摘Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.
文摘The purpose of this paper is to define a new symbol classand discuss the theory of two different pseudo-differential operators(p.d.o.)involving Fourier–Jacobi transform associated with a single symbol in.We also derive boundedness results for p.d.o.’s in Sobolev type space.Anewpseudo-differential operator is developed using the product of symbols.Finally,norm inequality for commutators between two pseudo-differential operators is obtained.
基金supported by the National Natural Science Foundation of China(Grant No.11901126)the Scientific Research Funds of Hunan Provincial Education Department.(Grant No.19B509).
文摘In this paper,the boundedness from Lebesgue space to Orlicz space of certain Toeplitz type operator related to the fractional and pseudo-differential operators is obtained.
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
基金funded by King Saud University,Riyadh,Saudi Arabia.
文摘Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.
