On a Local Mean Oscillation Decomposition

Abstract

In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calder\'{o}n-Zygmund singular integral operators $T$. These applications rely on the inequality $M^{\sharp}_{0,s}(Tf)(x) \leq c\,Mf(x)$, and we complete the results given here with a discussion of a local version of this estimate.Comment: 14 pages. Typos corrected, and Sections 2 and 5 are added. In particular, Section 2 contains a new proof of the pointwise inequality for singular integral