A T(1) Theorem for Fractional Sobolev Spaces on Domains

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Prats , M & Saksman , E 2017 , ' A T(1) Theorem for Fractional Sobolev Spaces on Domains ' , Journal of Geometric Analysis , vol. 27 , no. 3 , pp. 2490-2538 . https://doi.org/10.1007/s12220-017-9770-y

Title: A T(1) Theorem for Fractional Sobolev Spaces on Domains
Author: Prats, Marti; Saksman, Eero
Contributor organization: Department of Mathematics and Statistics
Date: 2017-07
Language: eng
Number of pages: 49
Belongs to series: Journal of Geometric Analysis
ISSN: 1050-6926
DOI: https://doi.org/10.1007/s12220-017-9770-y
URI: http://hdl.handle.net/10138/307530
Abstract: Given any uniform domain Omega, the Triebel-Lizorkin space F-p(s),(q)( Omega) with 0 <s <1 and 1 <p, q <infinity 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 <s <1 for any uniform domain and for a large family of Calderon-Zygmund operators in any ambient space R-d as long as sp > d.
Subject: Sobolev
Calder,n-Zygmund operators
Fourier multipliers
First-order differences
111 Mathematics
Peer reviewed: Yes
Rights: other
Usage restriction: openAccess
Self-archived version: acceptedVersion

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