Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1121-1131, 2022


The John-Nirenberg inequality for functions of bounded mean oscillation with bounded negative part

Min Hu, Dinghuai Wang

Received September 28, 2021.   Published online May 5, 2022.

Abstract:  A version of the John-Nirenberg inequality suitable for the functions $b\in{\rm BMO}$ with $b^-\in L^{\infty}$ is established. Then, equivalent definitions of this space via the norm of weighted Lebesgue space are given. As an application, some characterizations of this function space are given by the weighted boundedness of the commutator with the Hardy-Littlewood maximal operator.
Keywords:  bounded mean oscillation; commutator; Hardy-Littlewood maximal operator, John-Nirenberg inequality
Classification MSC:  42B35, 42B25
DOI:  10.21136/CMJ.2022.0362-21


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Affiliations:   Min Hu, School of Economics and Management, Anhui Normal University, Wuhu, 241002, P. R. China, email: humin@ahnu.edu.cn; Dinghuai Wang (corresponding author), School of Mathematics and Statistics, Anhui Normal University, Wuhu, 241002, P. R. China, e-mail: Wangdh1990@126.com


 
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