A T(1) theorem for fractional Sobolev spaces on domains
Given any uniform domain Ω, the Triebel-Lizorkin space Fsp,qpΩq with 0 ă s ă 1 and 1 ă p, q ă 8 can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(...
| Autores: | , |
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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:287736 |
| Acceso en línea: | https://ddd.uab.cat/record/287736 https://dx.doi.org/urn:doi:10.1007/s12220-017-9770-y |
| Access Level: | acceso abierto |
| Palabra clave: | Sobolev Triebel-Lizorkin Besov Calderón-Zygmund operators Fourier multipliers First-order differences |
| Sumario: | Given any uniform domain Ω, the Triebel-Lizorkin space Fsp,qpΩq with 0 ă s ă 1 and 1 ă p, q ă 8 can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this new characterization, we prove a T(1)-theorem for fractional Sobolev spaces with 0 ă s ă 1 for any uniform domain and for a large family of Calder'on-Zygmund operators in any ambient space Rd as long as sp ą d. |
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