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
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