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arXiv · 0812.2421

Non existence of principal values of signed Riesz transforms of non integer dimension

Aleix Ruiz de Villa·Xavier Tolsa
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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.

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Aleix Ruiz de Villa, Xavier Tolsa. 2008-12-12. Non existence of principal values of signed Riesz transforms of non integer dimension. https://arxiv.org/abs/0812.2421

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