Bulletin of the
Korean Mathematical Society
BKMS

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

Article

HOME ALL ARTICLES View

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.

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).

Stats or Metrics

Share this article on :

Related articles in BKMS