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(...

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Detalles Bibliográficos
Autores: Prats, Martí|||0000-0001-8799-6995, Saksman, Eero|||0000-0002-7630-7135
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
Descripción
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.