Non existence of principal values of signed Riesz transforms of non integer dimension
Abstract
In this paper we prove that, given s> 0, if E is a subset of Rm with positive and bounded s-dimensional Hausdorff measure Hs and the principal values of the s-dimensional signed Riesz transform of Hs|E exist Hs-almost everywhere in E, then s is integer. Other more general variants of this result are also proven.
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