In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy sp...In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy spaces.展开更多
参数满足什么条件时, Hilbert型级数不等式Σ^∞n=1Σ^∞m=1K(m,n)ambn≤M(Σ^∞m=1m^αa^p m )^1/p(Σ^∞n=1n^βb^qn )^1/q能够成立?而当Hilbert型级数不等式成立时,其常数因子又在什么条件下是最佳的?最佳常数因子的表达式是什么?这...参数满足什么条件时, Hilbert型级数不等式Σ^∞n=1Σ^∞m=1K(m,n)ambn≤M(Σ^∞m=1m^αa^p m )^1/p(Σ^∞n=1n^βb^qn )^1/q能够成立?而当Hilbert型级数不等式成立时,其常数因子又在什么条件下是最佳的?最佳常数因子的表达式是什么?这些问题的研究无疑是具有重要意义的.利用实分析的技巧及权函数方法,对具有齐次核的Hilbert型级数不等式的形式结构及参数关系进行了分析研究,得到其成立的充分必要条件和最佳常数因子的表达式.最后讨论了其结果在算子理论中的一些应用.展开更多
By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels...By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.展开更多
By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent ...By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.展开更多
基金supported by NSF of China(Grant:19971010)DPFIHE of China(Grant:98002703)National 973 Project of China
文摘In this paper.the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces,weak Hardy spaces and Herz-type Hardy spaces.
文摘参数满足什么条件时, Hilbert型级数不等式Σ^∞n=1Σ^∞m=1K(m,n)ambn≤M(Σ^∞m=1m^αa^p m )^1/p(Σ^∞n=1n^βb^qn )^1/q能够成立?而当Hilbert型级数不等式成立时,其常数因子又在什么条件下是最佳的?最佳常数因子的表达式是什么?这些问题的研究无疑是具有重要意义的.利用实分析的技巧及权函数方法,对具有齐次核的Hilbert型级数不等式的形式结构及参数关系进行了分析研究,得到其成立的充分必要条件和最佳常数因子的表达式.最后讨论了其结果在算子理论中的一些应用.
基金Supported by Guangdong Basic and Applied Basic Research Foundation Natural Science Foundation(Grant No.2021A1515010055)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.
基金Supported by National Natural Science Foundation of China(Grant No.12071491)Guangzhou Science and Technology Plan Project(Grant No.202102080177).
文摘By using the weight function method,the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K(n,||x||ρ,m)=G(nλ1||x||ρmλ,2)are discussed,some equivalent conditions of the optimal matching parameter are established,and the expression of the optimal constant factor is obtained.Finally,their applications in operator theory are considered.
