In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q ...In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = (α+β)/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p(R^n) is obtained.展开更多
In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space...In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.展开更多
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded...In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy (R+) to L^qxδ (R+) with the bound explicitly worked out.展开更多
In this paper, the λ-central BMO estimates for higher order commuta-tors of Hardy operators on central Morrey space Lq,λ(Rn) are established. In the meanwhile, the corresponding corollary for central BMO estimates...In this paper, the λ-central BMO estimates for higher order commuta-tors of Hardy operators on central Morrey space Lq,λ(Rn) are established. In the meanwhile, the corresponding corollary for central BMO estimates is also obtained.展开更多
In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are boun...In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of Hardy- Littlewood-Poly~ operator is also considered.展开更多
In this paper.a characterizationis,obtained for those pairs of weight funetions on (0=∞) for which the Hardy operator Pf(x)=f(t)dt is bounded from (μ) to ,0<q<1<p <+∞.
In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out...In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.展开更多
In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
In the setting of the Heisenberg group, based on the rotation method, we obtain the sharp (p,p) estimate for the Hardy operator. It will be shown that the norm of the Hardy operator on LP(Hn) is still p/(p- 1). ...In the setting of the Heisenberg group, based on the rotation method, we obtain the sharp (p,p) estimate for the Hardy operator. It will be shown that the norm of the Hardy operator on LP(Hn) is still p/(p- 1). This goes some way to imply that the Lp norms of the Hardy operator are the same despite the domains are intervals on R, balls in Rn, or ‘ellipsoids' on the Heisenberg group Hn. By constructing a special function, we find the best constant in the weak type (1, 1) inequality for the Hardy operator. Using the translation approach, we establish the boundedness for the Hardy operator from H1 to L1. Moreover, we describe the difference between Mp weights and Ap weights and obtain the characterizations of such weights using the weighted Hardy inequalities.展开更多
This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtai...This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators (with symbols in central BMO spaces) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.展开更多
The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, ...The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.展开更多
In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.
We obtain the operator norms of the n-dimensional fractional Hardy operator Hα(0 〈 α 〈 n) from weighted Lebesgue spaces Lp|x|p(R^n) to weighted weak Lebesgue spacesLq,∞|x|β(R^n).
This paper is a summary of the research on the characterizations of central function spaces by the author and his collaborators in the past ten years.More precisely,the author gives some characterizations of central C...This paper is a summary of the research on the characterizations of central function spaces by the author and his collaborators in the past ten years.More precisely,the author gives some characterizations of central Campanato spaces via the boundedness and compactness of commutators of Hardy operator.展开更多
The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractiona...The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractional Hardy operator with rough kernel.展开更多
In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and Hβ^*(x) of variable order β(x) on Herz spaces Kp(·)^α(·)q and Kp(·)^α(·)q′,where α(·) an...In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and Hβ^*(x) of variable order β(x) on Herz spaces Kp(·)^α(·)q and Kp(·)^α(·)q′,where α(·) and p(·)are both variable.展开更多
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金The NSF (Q2008A01) of Shandong,Chinathe NSF (10871024) of China
文摘In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα (R^n) is bounded from L^p(R^n) to L^q(R^n), where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = (α+β)/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p(R^n) is obtained.
基金supported by NSFC(11471309,11271162,and11561062)Project of Henan Provincial Department of Education(18A110028)+1 种基金the Nanhu Scholar Program for Young Scholars of XYNUDoctoral Scientific Research Startup Fund of Xinyang Normal University(2016)
文摘In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
基金Supported in part by the Natural Science Foundation of China under the Grant 10771221Natural Science Foundation of Beijing under the Grant 1092004
文摘In this paper, we establish two weighted integral inequalities for commutators of fractional Hardy operators with Besov-Lipschitz functions. The main result is that this kind of commutator, denoted by H^ab, is bounded from L^Pxy (R+) to L^qxδ (R+) with the bound explicitly worked out.
基金The Pre-research Project(SY201224) of Provincial Key Innovationthe Scientific and Technical Research Project(12531720) of the Education Department of Heilongjiang Province+1 种基金the NSF(A200913) of Heilongjiang Provincethe NSF(11041004,11161042,11071250) of China
文摘In this paper, the λ-central BMO estimates for higher order commuta-tors of Hardy operators on central Morrey space Lq,λ(Rn) are established. In the meanwhile, the corresponding corollary for central BMO estimates is also obtained.
基金The NSF(11261055)of Chinathe NSF(2012211B28,2011211A005)of Xinjiangthe Open Foundation Project(2012ZDXK002)of Key Disciplines in Xinjiang
文摘In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of Hardy- Littlewood-Poly~ operator is also considered.
文摘In this paper.a characterizationis,obtained for those pairs of weight funetions on (0=∞) for which the Hardy operator Pf(x)=f(t)dt is bounded from (μ) to ,0<q<1<p <+∞.
基金supported by National Natural Science Foundation of China(Grant Nos. 10931001,10901076 and 11171345)Shanghai Leading Academic Discipline Project(Grant No.J50101)supported by the Key Laboratory of Mathematics and Complex System(Beijing Normal University),Ministry of Education,China
文摘In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.
基金supported by National Natural Science Foundation of China (GrantNos. 10871024, 10901076)Natural Science Foundation of Shandong Province (Grant No. Q2008A01)+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)supported by the Key Laboratory of Mathematics and Complex System (Beijing Normal University), Ministry of Education,China
文摘In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
基金This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11271175, 11301248, 11401287), the Natural Science Foundation of Shandong Province (Grant No. ZR2012AQ026), and the AMEP of Linyi University.
文摘In the setting of the Heisenberg group, based on the rotation method, we obtain the sharp (p,p) estimate for the Hardy operator. It will be shown that the norm of the Hardy operator on LP(Hn) is still p/(p- 1). This goes some way to imply that the Lp norms of the Hardy operator are the same despite the domains are intervals on R, balls in Rn, or ‘ellipsoids' on the Heisenberg group Hn. By constructing a special function, we find the best constant in the weak type (1, 1) inequality for the Hardy operator. Using the translation approach, we establish the boundedness for the Hardy operator from H1 to L1. Moreover, we describe the difference between Mp weights and Ap weights and obtain the characterizations of such weights using the weighted Hardy inequalities.
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators (with symbols in central BMO spaces) are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
基金Supported by National Natural Science Foundation of China (Grant No. 10871024)
文摘The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.
基金supported by the National Natural Science Foundation of China(Grant No.11761026)Guangxi Natural Science Foundation(Grant No.2020GXNSFAA159085).
文摘In this paper,we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of two weighted Herz spaces.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.11771195)the Key Laboratory of Mathematics and Complex System of Beijing Normal University.
文摘This paper is a summary of the research on the characterizations of central function spaces by the author and his collaborators in the past ten years.More precisely,the author gives some characterizations of central Campanato spaces via the boundedness and compactness of commutators of Hardy operator.
基金supported by the NSF of China(Grant Nos.11771195,and 12071197)the NSF of Shandong Province(Grant Nos.ZR2019YQ04,2020KJI002,and 2019KJI003)the key Laboratory of Complex Systems and Intelligent Computing in University of Shandong(Linyi University).
文摘The more explicit decomposition of the operator and the kernel are utilized to investigate a characterization of the central BMO(R^(n))-closure of C^(∞)(R^(n))space via the compactness of the commutators of fractional Hardy operator with rough kernel.
基金Supported by the National Natural Science Foundation of China(11201003)Supported by the Education Committee of Anhui Province(KJ2012A133)
文摘In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β(x) on variable exponent Herz-Morrey spaces.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and Hβ^*(x) of variable order β(x) on Herz spaces Kp(·)^α(·)q and Kp(·)^α(·)q′,where α(·) and p(·)are both variable.