Non existence of principal values of signed Riesz transforms of non integer dimension
Classical Analysis and ODEs
2008-12-15 v1 Functional Analysis
Abstract
In this paper we prove that, given s> 0, if E is a subset of R^m with positive and bounded s-dimensional Hausdorff measure H^s and the principal values of the s-dimensional signed Riesz transform of H^s|E exist H^s-almost everywhere in E, then s is integer. Other more general variants of this result are also proven.
Keywords
Cite
@article{arxiv.0812.2421,
title = {Non existence of principal values of signed Riesz transforms of non integer dimension},
author = {Aleix Ruiz de Villa and Xavier Tolsa},
journal= {arXiv preprint arXiv:0812.2421},
year = {2008}
}