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Bull. Korean Math. Soc. 2022; 59(3): 547-566

Published online May 31, 2022 https://doi.org/10.4134/BKMS.b201019

Copyright © The Korean Mathematical Society.

The characterisation of $BMO$ via commutators in variable Lebesgue spaces on stratified groups

Dongli Liu, Jian Tan, Jiman Zhao

Beijing Normal University; Nanjing University of Posts and Telecommunications; Beijing Normal University

Abstract

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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