On a Local Mean Oscillation Decomposition

Jonathan Poelhuis, Alberto Torchinsky

Published 2012-08-30, updated 2013-01-27Version 2

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.