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 paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^...In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.展开更多
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）.
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
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, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i =...In this paper, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2,..., l.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 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.
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
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This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10571014,10371080)the Doctoral Programme Foundation of Institute of Higher Education of China(Grant No.20040027001)
文摘In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^n)function,where 1/p1-1/p2=β/n,1<p1<∞,0≤β<n.Furthermore, the characterization of H_(β,b)on the homogenous Herz space K_q^(α,p)(R^n)was obtained.
基金Supported Partially by NSF of China (10371087) Education Committee of Anhui Province (2003kj034zd).
文摘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.
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Supported in part by the NNSF of China under grant #10771110 and #10471069sponsored by the NSF of Ningbo city under grant #2009A610090
文摘In this paper, we prove the boundedness from H1 （Rn） to Ln/n-α∞, （Rn） for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2,..., l.
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 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.
