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arXiv · 1208.6184

On a Local Mean Oscillation Decomposition

Jonathan Poelhuis·Alberto Torchinsky
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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.

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Jonathan Poelhuis, Alberto Torchinsky. 2012-08-30. On a Local Mean Oscillation Decomposition. https://arxiv.org/abs/1208.6184

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