J. Korean Math. Soc. 2022; 59(3): 495-517
Online first article April 13, 2022 Printed May 1, 2022
https://doi.org/10.4134/JKMS.j210188
Copyright © The Korean Mathematical Society.
Qianjun He, Juan Zhang
Beijing Information Science and Technology University; Beijing Forestry University
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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