与球 Banach 函数空间相关的广义 Morrey 空间上的双线性 Caldero′n-Zygumd 算子 及其交换子的有界性
Boundedness of Bilinear C - Z Operatorsand Its Commutator Generated by onGeneralized Morrey Spaces Associated with Ball Banach Function Spaces
DOI: 10.12677/PM.2023.135121, PDF, HTML, 下载: 195  浏览: 405  科研立项经费支持
作者: 李雪梅：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 双线性 Caldero′n-Zygumd 算子；交换子；球 Banach 函数空间；广义 Morrey 空间；有界性；Bilinear C ? Z Operator； Commutator； Ball Banach Function Spaces； Generalized Morrey Space； Boundedness
摘要: 本文主要讨论了双线性 C−Z 算子 T 及其交换子 [b1, b2, T ] 在与球 Banach 函数空间相关的广义 Morrey 空间 Mu(X) 上的有界性. 证明了 T 从乘积空间 Mu1 (X1) × Mu2 (X2) 到空间 Mu(Y ) 有界. 进一步, 也证明了由 b1, b2 ∈ BMO(X) 和 T 生成的交换子 [b1, b2, T ] 是从乘积空间 Mu1 (X1) × Mu2 (X2) 到空间 Mu(Y ) 有界的, 其中 u = u1u2.
Abstract: In this paper, the authors mainly discuss the boundedness of bilinear C−Z operator T and its commutator [b1, b2, T ] on generalized Morrey spaces associated with ball Banach function spaces Mu(X). The authors prove bilinear C−Z operator T is bounded from product spaces Mu1 (X1) × Mu2 (X2) into spaces Mu(Y ). Further, they also prove that the commutator [b1, b2, T ] generated by b1, b2 ∈ BMO(X) and T are bounded from product spaces Mu1 (X1) × Mu2 (X2) into spaces Mu(Y ), where u = u1u2.
文章引用：李雪梅. 与球 Banach 函数空间相关的广义 Morrey 空间上的双线性 Caldero′n-Zygumd 算子 及其交换子的有界性[J]. 理论数学, 2023, 13(5): 1157-1172. https://doi.org/10.12677/PM.2023.135121

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