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Sobolev regularity of the Beurling transform on planar domains
Prats Soler, Martí (Universidad Autónoma de Madrid. Departamento de Matemáticas)

Date: 2017
Abstract: Consider a Lipschitz domain Ω and the Beurling transform of its characteristic function BχΩ(z) = −p. v. 1 πz2 ∗ χΩ(z). It is shown that if the outward unit normal vector N of the boundary of the domain is in the trace space of Wn,p(Ω) (i. e. , the Besov space Bn−1/p p,p (∂Ω)) then BχΩ ∈ Wn,p(Ω). Moreover, when p > 2 the boundedness of the Beurling transform on Wn,p(Ω) follows. This fact has farreaching consequences in the study of the regularity of quasiconformal solutions of the Beltrami equation.
Rights: Tots els drets reservats
Language: Anglès.
Document: article ; recerca ; publishedVersion
Subject: Quasiconformal mappings ; Sobolev spaces ; Lipschitz domains ; Beurling transform ; David-Semmes betas ; Peter Jones' betas
Published in: Publicacions matemàtiques, Vol. 61 Núm. 2 (2017) , p. 291-336 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/327583
DOI: 10.5565/PUBLMAT6121701


46 p, 1.5 MB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles

 Record created 2017-09-04, last modified 2020-04-25



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