We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is ...We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.展开更多
In this paper, by applying a vector-valued inequality we obtained a decomposition theorem on Herz spaces over locally compact Vilenkin groups with new range 0<q≤1.
Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on ...Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.展开更多
The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also cons...The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered.展开更多
It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to ...It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to K· α,p q(R n); if α=n(1-1q)+β then μ Ω(f)(x) is boundedness from H K· α,p q(R n) to W K· α,p q(R n).展开更多
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.
Abstract The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧κα,p,q（R）, α ∈R and 1≤〈 p, q ≤∞, in the context of Dunkl harmonic analysis.
In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the...In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.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
基金Supported by Natural Science Foundation of Anhui Higher Education Institutions(Grant No.KJ2021A1050).
文摘We consider multilinear commutators of singular integrals de ned by T→bf(x)=∫R^(n)mПi=1(bi(x)-bi(y))K(x,y)f(y)dy,where K is a standard Calderon-Zygmund kernel,m is a positive integer and~b=(b_(1);b_(2);…;b_(m))is a family of m locally integrable functions.Based on the theory of variable exponent and on generalization of the BMO norm,we prove the boundedness of multilinear commutators T_(b) on grand variable Herz spaces.The result is still new even in the special case of m=1.
基金Supported by the Natural Science Foundation of Zhejiang Province(102005)Supported by the Natural Science Foundation of Henan University(XK03YBSX002)
文摘In this paper, by applying a vector-valued inequality we obtained a decomposition theorem on Herz spaces over locally compact Vilenkin groups with new range 0<q≤1.
基金Supported by Natural Science Foundation of Xinjiang University Supported by the NNSF of Chlna（10861010） Supported by Research Starting Foundation for Doctors of Xinjiang University（BS090102）
文摘Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.
基金The second author was supported by NNSF of China (10371004)the third author was supported by the NNSF of China (60474070)
文摘The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered.
文摘It provides the boundary proof of Marcnkiewicz integral μ Ω(f)(x) on Herz_type Hardy spaces. That is: if n(1-1q)≤α【n(1-1q)+β then μ Ω(f)(x) is boundendess from H K· α,p q(R n) to K· α,p q(R n); if α=n(1-1q)+β then μ Ω(f)(x) is boundedness from H K· α,p q(R n) to W K· α,p q(R n).
文摘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.
文摘Abstract The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧κα,p,q（R）, α ∈R and 1≤〈 p, q ≤∞, in the context of Dunkl harmonic analysis.
基金This project is supported by the National 973Project(G199907510)the SEDF of China(20010027002)
文摘In this paper, the authors study two classes of multilinear singular integrals and obtain their boundedness from Lebesgue spaces to Lipschitz spaces and from Herz type spaces to central Campanato spaces. Moreover, the authors also consider the extreme cases.
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.
