广义加权变指标Morrey空间上双线性θ-型Calderón-Zygmund算子

doi:10.6040/j.issn.1671-9352.0.2022.624

摘要/Abstract

摘要：

利用双线性θ-型Calderón-Zygmund算子在变指标Lebesgue空间的有界性以及函数空间控制关系，以及在假设函数u满足某些特定的条件下，证明双线性θ-型Calderón-Zygmund算子从乘积广义加权变指标Morrey空间到广义加权变指标Morrey空间上有界；同时也证明由双线性θ-型Calderón-Zygmund算子和b₁, b₂ ∈ BMO(Rⁿ)生成的交换子在广义加权变指标Morrey空间上是有界的。

关键词: Morrey型空间, 加权, 变指标, Calderón-Zygmund算子, 交换子, BMO空间

Abstract:

Via the boundedness of the bilinear θ-type Calderón-Zygmund operators in the variable index Lebesgue space and the control relations in the function spaces, and assuming that the functions u meet certain conditions, the authors prove that the bilinear θ-type Calderón-Zygmund operators are bounded from product generalized weighted variable exponent Morrey spaces to generalized weighted variable exponent Morrey spaces. Furthermore, the authors also prove that the commutators generated by the bilinear θ-type Calderón-Zygmund operators and b₁, b₂ ∈ BMO(Rⁿ) are bounded on generalized weighted variable exponent Morrey spaces.

Key words: Morrey type space, weighted, variable exponent, Calderón-Zygmund operator, commutator, BMO space

中图分类号:

O174.2

芮俪,逯光辉,李雪梅. 广义加权变指标Morrey空间上双线性θ-型Calderón-Zygmund算子[J]. 《山东大学学报(理学版)》, 2024, 59(4): 62-72.

Li RUI,Guanghui LU,Xuemei LI. Bilinear θ-type Calderón-Zygmund operators on generalized weighted variable exponent Morrey spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 62-72.

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