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Keywords:
bounded mean oscillation; commutator; Hardy-Littlewood maximal operator, John-Nirenberg inequality
bounded mean oscillation; commutator; Hardy-Littlewood maximal operator, John-Nirenberg inequality
Summary:
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.
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