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J. Korean Math. Soc. 2022; 59(3): 495-517

Published online May 1, 2022 https://doi.org/10.4134/JKMS.j210188

Copyright © The Korean Mathematical Society.

On weighted compactness of commutators of bilinear fractional maximal operator

Qianjun He, Juan Zhang

Beijing Information Science and Technology University; Beijing Forestry University

Abstract

Let $\mathcal{M}_{\alpha}$ be a bilinear fractional maximal operator and $BM_{\alpha}$ be a fractional maximal operator associated with the bilinear Hilbert transform. In this paper, the compactness on weighted Lebesgue spaces are considered for commutators of bilinear fractional maximal operators; these commutators include the fractional maximal linear commutators $\mathcal{M}_{\alpha,b}^{j}$ and $BM_{\alpha, b}^{j} $ $(j=1,2)$, the fractional maximal iterated commutator $\mathcal{M}_{\alpha,\vec{b}}$, and $BM_{\alpha, \vec{b}}$, where $b\in{\rm BMO}(\mathbb{R}^{d})$ and $\vec{b}=(b_{1},b_{2})\in{\rm BMO}(\mathbb{R}^{d})\times {\rm BMO}(\mathbb{R}^{d})$. In particular, we improve the well-known results to a larger scale for $1/2

Keywords: Bilinear fractional maximal operators, commutators, compactness, weighted esitmates

MSC numbers: Primary 42B25, 47B07; Secondary 42B20

Supported by: The first author was in part supported by National Natural Science Foundation of China (Nos. 11871452, 12071473) and the second author was supported by National Natural Science Foundation of China (No. 12101049).

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