Bull. Korean Math. Soc. 2022; 59(3): 547-566
Online first article May 11, 2022 Printed May 31, 2022
https://doi.org/10.4134/BKMS.b201019
Copyright © The Korean Mathematical Society.
Dongli Liu, Jian Tan, Jiman Zhao
Beijing Normal University; Nanjing University of Posts and Telecommunications; Beijing Normal University
Let $T$ be a bilinear Calder\'{o}n-Zygmund operator, $$b\in \cup_{q>1}L_{loc}^{q}(G).$$ We firstly obtain a constructive proof of the weak factorisation of Hardy spaces. Then we establish the characterization of $BMO$ spaces by the boundedness of the commutator $[b, T]_{j}$ in variable Lebesgue spaces.
Keywords: Bilinear Calder\'{o}n-Zygmund operators, variable Lebesgue spaces, stratified groups
MSC numbers: Primary 42B20, 42B35, 43A80
Supported by: Jiman Zhao is supported by the National Key Research and Development Program of China (No.2020YFA0712900) and National Natural Science Foundation of China (Nos.11471040 and 11761131002). Jian Tan is supported by National Natural Science Foundation of China (No.11901309), Natural Science Foundation of Jiangsu Province of China (BK20180734), Natural Science Research of Jiangsu Higher Education Institutions of China (18KJB110022) and Nanjing University of Posts and Telecommunications Science Foundation (NY219114).
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