Sobolev regularity of the Beurling transform on planar domains
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). Moreov...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:180442 |
| Acceso en línea: | https://ddd.uab.cat/record/180442 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6121701 |
| Access Level: | acceso abierto |
| Palabra clave: | Quasiconformal mappings Sobolev spaces Lipschitz domains Beurling transform David-Semmes betas Peter Jones' betas |
| Sumario: | 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. |
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