The natural maximal operator on BMO
The natural maximal operator on BMO
We introduce a generalization of the Hardy-Littlewood maximal operator, the natural maximal operator $M^\natural$, in some sense the maximal operator which most naturally commutes pointwise with the logarithm on $A^\infty$. This commutation reveals the behavior of $M\!: A^\infty \rightarrow A^1$ to directly correspond to that of $M^\natural \!: B\! M\! …