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 Calderón-Zygmund singular integral operators $T$. These applications rely on the inequality $M_{0,s}^{♯}(Tf)(x)\le cMf(x)$, and we complete the results given here with a discussion of a local version of this estimate.

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 integrals