Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online May 11, 2022

Copyright © The Korean Mathematical Society.

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

Dongli Liu, Jian Tan, and Jiman Zhao

Beijing Normal University, Nanjing University of Posts and Telecommunications

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: 42B20; 42B35; 43A80

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