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

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dc.creatorde Villa, Aleix Ruiz
dc.creatorTolsa, Xavier
dc.date2008-12-12
dc.date.accessioned2026-07-07T12:12:27Z
dc.date.available2026-07-07T12:12:27Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/0812.2421
dc.identifierhttp://arxiv.org/abs/0812.2421
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210550
dc.subjectClassical Analysis and ODEs
dc.subjectFunctional Analysis
dc.subject28A75; 31B10; 42B25
dc.titleNon existence of principal values of signed Riesz transforms of non integer dimension
dc.typetext

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