• 论文 •

### 具有广义核的多线性平方算子与交换子的加权估计

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
• Supported by:
the NSFC(11971209);the NSFC(11961032);the NSF of Jiangxi Province(20192BAB201003)

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.

• O174.2