On a Local Mean Oscillation Decomposition

Jonathan Poelhuis; Alberto Torchinsky

On a Local Mean Oscillation Decomposition

Classical Analysis and ODEs 2013-01-29 v2

Authors: Jonathan Poelhuis , Alberto Torchinsky

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.

Keywords

wavelet and multifractal analysis operator theory and elliptic operators function spaces and inequalities

Cite

@article{arxiv.1208.6184,
  title  = {On a Local Mean Oscillation Decomposition},
  author = {Jonathan Poelhuis and Alberto Torchinsky},
  journal= {arXiv preprint arXiv:1208.6184},
  year   = {2013}
}

Comments

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

On a Local Mean Oscillation Decomposition

Abstract

Keywords

Cite

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