数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 954-967.

• 论文 • 上一篇    下一篇

具有广义核的多线性平方算子与交换子的加权估计

陈晓莉(),陈冬香(),朱红燕   

  1. 江西师范大学数学与统计学院 南昌 330022
  • 收稿日期:2020-03-27 出版日期:2021-08-26 发布日期:2021-08-09
  • 作者简介:陈晓莉, E-mail: littleli_chen@163.com|陈冬香, E-mail: chendx020@163.com
  • 基金资助:
    国家自然科学基金(11971209);国家自然科学基金(11961032);江西省自然科学基金(20192BAB201003)

Weighted Estimates for Some Multilinear Square Operator and Commutator with Generalized Kernel

Xiaoli Chen(),Dongxiang Chen(),Hongyan Zhu   

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
  • Received:2020-03-27 Online:2021-08-26 Published:2021-08-09
  • Supported by:
    the NSFC(11971209);the NSFC(11961032);the NSF of Jiangxi Province(20192BAB201003)

摘要:

该文研究了一类具有广义积分核的多线性平方算子,证明了该多线性平方算子$T$$(L^{p_1}(\omega_1)\times\cdots\times L^{p_m}(\omega_m))$$L^{p}(\nu_{\omega})$上有界,其中$\frac{1}{p_1}+\cdots+\frac{1}{p_m}=\frac{1}{p},\nu_{\omega}=\prod\limits_{i=1}^m\omega_i^{\frac{p_i}{p}}$.同时该文还证明了多线性平方算子$T$和BMO函数生成的交换子$T_{\sum b}$也是$(L^{p_1}(\omega_1)\times\cdots\times L^{p_m}(\omega_m))$$L^{p}(\nu_{\omega})$上有界算子.最后证明了多线性平方算子$T$$L^{\infty}\times\cdots\times L^{\infty}$$BMO$上的有界算子,推广了一些已知的结果.

关键词: 广义积分核, 多线性平方算子, Sharp极大函数, 交换子,

Abstract:

In this paper, the authors investigate some multilinear square operator with generalized kernel. They prove that the multilinear square operator $T$ is bounded from $(L^{p_1}(\omega_1)\times\cdots\times L^{p_m}(\omega_m))$ into $L^{p}(\nu_{\omega})$, where $\frac{1}{p_1}+ \cdots+\frac{1}{p_m}=\frac{1}{p}, \nu_{\omega}=\prod\limits_{i=1}^m\omega_i^{\frac{p_i}{p}} $, the authors proved the commutator $T_{\sum b}$, generalized by multilinear square operator $T$ and BMO function, is also bounded from$(L^{p_1}(\omega_1)\times\cdots\times L^{p_m}(\omega_m))$ into $L^{p}(\nu_{\omega})$上. Finally, the authors also prove the multilinear square operator $T$ is bounded from $L^\infty\times\cdots\times L^{\infty}$ into $BMO$. Some known results are improved.

Key words: Generalized integral kernel, Multilinear square operator, Sharp maximal function, Commutator, Weight

中图分类号: 

  • O174.2