Lp-estimates for the variation for singular integrals on uniformly rectifiable sets

Abstract

The $L^p$ ($1<p<\infty$) and weak-$L^1$ estimates for the variation for Calderón-Zygmund operators with smooth odd kernel on uniformly rectifiable measures are proven. The $L^2$ boundedness and the corona decomposition method are two key ingredients of the proof.

33 pages