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

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

2008-12-12

arxiv.org/abs/0812.2421v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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