Sobolev regularity of the Beurling transform on planar domains
Prats, 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 ; Versió publicada |
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 alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/327583
DOI: 10.5565/PUBLMAT6121701
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Record created 2017-09-04, last modified 2024-04-05