Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems o...The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems of these operators in (1≤p≤∞) and obtain complete results.展开更多
In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the G...In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication...Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.展开更多
The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind o...The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind of the homogeneous type spaces.展开更多
A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p 【 ∞, a 】 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an abs...A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p 【 ∞, a 】 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute constant depending only on the parameter a.展开更多
In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b...In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.展开更多
LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of consi...LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.展开更多
This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, B...This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）展开更多
In this paper, we give the characteristics of the coefficient multipliers from H p,G p,B p(0【p【1) and A p(0【p≤1) to G q(1≤q【∞), from G p to G q(1≤p≤q【∞).
This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt...This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).展开更多
Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A o...Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.展开更多
In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to ...This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.展开更多
In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatte...In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.展开更多
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems of these operators in (1≤p≤∞) and obtain complete results.
基金Supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province in China(2022JJ30369)。
文摘In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
基金supported by NSFC(No.11301203)NSFC(No.11371057,11471033)+5 种基金NSFC(No.11371158)the Fundamental Research Funds for the Central Universities(CCNU-14A05037)the Fundamental Research Funds for the Central Universities(No.2014KJJCA10)SRFDP(No.20130003110003)the program for Changjiang ScholarsInnovative Research Team in University(No.IRT13066)
文摘Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.
文摘The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind of the homogeneous type spaces.
基金Supported by the Unidade de Investigao "Matemtica e Aplicaoes" of University of Aveiro, National Natural Science Foundation of China (Grant No. 10771201)New Century Excellent Talentsin University (Grant No. 05-0539)
文摘A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p 【 ∞, a 】 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute constant depending only on the parameter a.
文摘In this paper we prove the following Hajek Renyi inequality:Let 0<p≤1 ,then for any Banach space B , any L p integrable B valued random variable sequence {D n,n≥1} ,any real number sequence {b n,n≥1} with 0<b n↑∞ ,any integer n≥1 ,there exits a constant C=C p>0 (only depending on p ) such thatP( sup j≥nji=1D ib j≥ε)≤Cε -p (∞j=n+1E‖D j‖ pb p j+nj=1E‖D j‖ pb p n) In the other direction,we prove some strong laws of large numbers and the integrability of the maximal functions for B valued random variable sequences by using this inequality and the Hajeck Renyi inequality we have obtained recently.Some known results are extended and improved.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.
基金Supported in part by the National Natural Science Foundation of China(11271359)the Fundamental Research Funds for the Central Universities(2014-Ia-037and 2015-IVA-069)
文摘This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F（p, q, s） spaces in the unit ball of C^n which contain many classical function spaces, such as the Bloch space, BMOA and Q8 spaces. The boundedness and compactness of these operators on F（p, q, s） spaces are characterized by means of an embedding theorem, i.e., F（p,q, s） spaces boundedly embedded into the tent-type spaces Tp,s^∞（μ）
文摘In this paper, we give the characteristics of the coefficient multipliers from H p,G p,B p(0【p【1) and A p(0【p≤1) to G q(1≤q【∞), from G p to G q(1≤p≤q【∞).
基金Supported by the NNSF of China(10771064, 11101139)Supported by the NSF of Zhejiang Province(Y7080197, Y6090036, Y6100219)Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province(T200924)
文摘This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).
文摘Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.
文摘In this paper,we construct a function u in L2,1（Bn,dA）,which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D（Bn,dA）.Furthermore,Schatten p-class（0〈p〈∞） Toeplitz operators on Dirichlet space D（Bn,dA） with unbounded symbols are also obtained.
