Geodesic
The John-Nirenberg inequality for functions of bounded mean oscillation with bounded negative part
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1121-1131.

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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.
DOI : 10.21136/CMJ.2022.0362-21
Classification : 42B25, 42B35
Keywords: bounded mean oscillation; commutator; Hardy-Littlewood maximal operator, John-Nirenberg inequality 
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Hu, Min; Wang, Dinghuai. The John-Nirenberg inequality for functions of bounded mean oscillation  with bounded negative part. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1121-1131. doi : 10.21136/CMJ.2022.0362-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0362-21/

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