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Fractional integration associated with second order divergence operators on R^n 被引量:3
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作者 邓东皋 颜立新 《Science China Mathematics》 SCIE 2003年第3期355-363,共9页
The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (?Δ)?α/2 are extended to the generalised fractional integrals L –α/2 for 0 < α < n, where L=?div A? is a uniformly complex elliptic opera... The classical Hardy-Littlewood-Sobolev theorems for Riesz potentials (?Δ)?α/2 are extended to the generalised fractional integrals L –α/2 for 0 < α < n, where L=?div A? is a uniformly complex elliptic operator with bounded measurable coefficients in ?n. 展开更多
关键词 fractional integral second order divergence operator SEMIGROUP Hardy- Littlewood- Sobolev theorem
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FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS 被引量:1
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作者 DENGDONGGAO XUMING YANLIXIN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2005年第2期229-238,共10页
The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L?α/2 for 0 < α < n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn.
关键词 fractional integrals Higher order elliptic operator Hardy-Littlewood- Sobolev theorem
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Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China 被引量:1
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作者 Yong-Bin Wang Si-Yu Qing +3 位作者 Zi-Yue Liang Chang Ma Yi-Chun Bai Chun-Jie Xu 《World Journal of Gastroenterology》 SCIE CAS 2023年第42期5716-5727,共12页
BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their s... BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA. 展开更多
关键词 HEPATITIS Seasonal autoregressive fractionally integrated moving average Seasonal autoregressive integrated moving average Prediction EPIDEMIC Time series analysis
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THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES
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作者 韩妍妍 伍火熊 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期1981-1996,共16页
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th... This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn). 展开更多
关键词 fractional type Marcinkiewicz integrals COMMUTATORS Muckenhoupt weights BMO spaces Hardy spaces
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A Technique for Estimation of Box Dimension about Fractional Integral
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作者 Ruhua Zhang 《Advances in Pure Mathematics》 2023年第10期714-724,共11页
This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary... This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals. 展开更多
关键词 Upper Box Dimension Riemann-Liouville fractional Integral Fractal Continuous Function Box Dimension
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THE HADAMARD INEQUALITY FOR CONVEX FUNCTION VIA FRACTIONAL INTEGRALS 被引量:4
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作者 M.E.ZDEMR S.S.DRAGOMIR C.YILDIZ 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1293-1299,共7页
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
关键词 Hadamard's inequality convex functions power-mean inequality Riemann-Liouville fractional integration
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BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATI ON ONHERZ-TYPE SPACES 被引量:1
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作者 刘宗光 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期461-470,共10页
This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
关键词 Herz space weak Herz space Herz-type Hardy space fractional integration BMO(Rn) function COMMUTATOR
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Modeling Seasonal Fractionally Integrated Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroscedasticity Model with Seasonal Level Shift Intervention
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作者 Lawrence Dhliwayo Florance Matarise Charles Chimedza 《Open Journal of Statistics》 2020年第5期810-831,共22页
This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-<... This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">generalized conditional heteroskedastisticty (SARFIMA-</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">GARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modeling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> derived. Test statistics that are useful to examine if seasonal level shift in a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> SARFIMA-GARCH model </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> also considered.</span> 展开更多
关键词 SEASONALITY fractional integration LONG-MEMORY Level Shift SLS-SARFIMA SLS-GARCH VOLATILITY
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Boundedness for multilinear fractional integral operators on Herz type spaces 被引量:5
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作者 SHI Yan-long TAO Xiang-xing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期437-446,共10页
In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for cl... In this paper the boundedness for the multilinear fractional integral operator Iα^(m) on the product of Herz spaces and Herz-Morrey spaces are founded, which improves the Hardy- Littlewood-Sobolev inequality for classical fractional integral Iα. The method given in the note is useful for more general multilinear integral operators. 展开更多
关键词 multilinear fractional integral Herz space homogeneous Herz-Morrey space product space
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A∞ weight estimates for vector-valued commutators of multilinear fractional integral 被引量:3
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作者 YU Xiao CHEN Jie-cheng ZHANG Yan-dan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第3期335-357,共23页
In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the bo... In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained. 展开更多
关键词 VECTOR-VALUED COMMUTATOR multilineax fractional integral weighted.
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Boundedness of fractional integral operators on α-modulation spaces 被引量:3
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作者 WU Xiao-mei CHEN Jie-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第3期339-351,共13页
In this paper, we obtain the boundedness of the fractional integral operators, the bilineax fractional integral operators and the bilinear Hilbert transform on α-modulation spaces.
关键词 α-modulation space fractional integral operator bilinear fractional integral operator bilinearHilbert transform.
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GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY 被引量:3
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作者 魏含玉 夏铁成 《Acta Mathematica Scientia》 SCIE CSCD 2014年第1期53-64,共12页
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup... Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 展开更多
关键词 generalized fractional trace variational identity fractional integrable couplings soliton hierarchy Hamiltonian structure
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Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces 被引量:3
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作者 Hua Wang 《Analysis in Theory and Applications》 2013年第1期72-85,共14页
Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn... Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k(w) when the symbol b belongs to BMO(Rn) or the homogeneous Lipschitz space. 展开更多
关键词 Gaussian upper bound fractional integral weighted Morrey space commutator.
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ENDPOINT ESTIMATES FOR FRACTIONAL INTEGRAL ASSOCIATED TO SCHRDINGER OPERATORS ON THE HEISENBERG GROUPS 被引量:2
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作者 江寅生 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期993-1000,共8页
Let ∠= -△Hn+ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates o... Let ∠= -△Hn+ V be the Schrdinger operator on the Heisenberg groups Hn,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠. 展开更多
关键词 Schrdinger operator Heisenberg group BMO_∠ BLO_∠ fractional integral
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FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS 被引量:2
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作者 Yaghoub JALILIAN 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1317-1330,共14页
In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ... In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations. 展开更多
关键词 fractional integral inequality existence of solution Caputo fractional derivative fractional differential equation fixed point
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Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives 被引量:3
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作者 王琳莉 傅景礼 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期277-280,共4页
In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagran... In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results. 展开更多
关键词 fractional cyclic integral fractional Routh equation combined Caputo fractional derivative
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FRACTIONAL INTEGRALS WITH VARIABLE KERNELS ON HARDY SPACES 被引量:2
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作者 ZhangPu DingYong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第4期461-466,共6页
The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i... The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002. 展开更多
关键词 fractional integral variable kernel Dini-condition Hardy space
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CBMO Estimates for Commutators of Fractional Integral Operators with Variable Kernels 被引量:2
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作者 WANG Li-wei SHU Li-sheng QU Meng 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期68-73,共6页
In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish th... In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces. 展开更多
关键词 CBMO Morrey-Herz space fractional integral COMMUTATOR variable kernel
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BOUNDEDNESS OF HIGHER ORDER COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON HARDY SPACES 被引量:2
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作者 Chunlei He Lisheng Shu 《Analysis in Theory and Applications》 2005年第3期249-257,共9页
Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-t... Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces. 展开更多
关键词 (θ - N)-type fractional integral operator COMMUTATOR BMO space Hardy space Herz-type Hardy space ATOM
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WEIGHTED L^p BOUNDEDNESS FOR MULTILINEAR FRACTIONAL INTEGRAL ON PRODUCT SPACES 被引量:2
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作者 Yanlong Shi Xiangxing Tao 《Analysis in Theory and Applications》 2008年第3期280-291,共12页
For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= (y1, Y2,…, ym) and 7 denotes the m-tuple (f1, f2,…, fm). In this note, the one- weighted and ... For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= (y1, Y2,…, ym) and 7 denotes the m-tuple (f1, f2,…, fm). In this note, the one- weighted and two-weighted boundedness on Lp (JRn) space for multilinear fractional integral operator I(am) and the fractional multi-sublinear maximal operator Mα(m) are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα(m). 展开更多
关键词 multilinear fractional integral multilinear fractional maximal function Ap q a weight Ap q weight
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