Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 954-967.

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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)


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

CLC Number: 

  • O174.2