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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 62-72.doi: 10.6040/j.issn.1671-9352.0.2022.624

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

芮俪(),逯光辉*(),李雪梅   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2022-11-28 出版日期:2024-04-20 发布日期:2024-04-12
  • 通讯作者: 逯光辉 E-mail:r495560215@163.com;luguanghui@nwnu.edu.cn
  • 作者简介:芮俪(1997—)，女，硕士研究生，研究方向为调和分析. E-mail：r495560215@163.com
  • 基金资助:
    国家自然科学基金资助项目(12201500);甘肃省青年科技基金计划资助项目(22JR5RA173);甘肃省优秀研究生“创新之星”资助项目(2022CXZX-327)

Bilinear θ-type Calderón-Zygmund operators on generalized weighted variable exponent Morrey spaces

Li RUI(),Guanghui LU*(),Xuemei LI   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-11-28 Online:2024-04-20 Published:2024-04-12
  • Contact: Guanghui LU E-mail:r495560215@163.com;luguanghui@nwnu.edu.cn

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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
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