A T(1) theorem for fractional Sobolev spaces on domains
Prats, Martí (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Saksman, Eero (University of Helsinki. Department of Mathematics and Statistics)

Date:	2017
Abstract:	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.
Grants:	European Commission 320501 Ministerio de Economía y Competitividad MTM2013-44304-P Ministerio de Ciencia e Innovación MTM-2010-16232 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-75 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/FI-B2 00107
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Sobolev ; Triebel-Lizorkin ; Besov ; Calderón-Zygmund operators ; Fourier multipliers ; First-order differences
Published in:	Journal of Geometric Analysis, Vol. 27 (2017) , p. 2490-2538, ISSN 1559-002X

DOI: 10.1007/s12220-017-9770-y

Postprint 38 p, 727.7 KB

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