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Spring 2005 Modulus of continuity of the Mazur map between unit balls of Orlicz spaces and approximation by Hölder mappings
Sylvain Delpech
Illinois J. Math. 49(1): 195-216 (Spring 2005). DOI: 10.1215/ijm/1258138314

Abstract

Under some regularity assumptions, we compute the modulus of continuity of the generalized Mazur map between unit balls of Orlicz spaces. Our estimate coincides with the known estimates in the setting of $L_p(\mu)$-spaces. We apply this estimate to approximate uniformly continuous mappings between balls of reflexive Orlicz spaces by $\alpha$-Hölder maps, with $\alpha$ as large as possible. We also relate this optimal value of $\alpha$ to the Boyd indices of the spaces and to the problem of isomorphic extension of Hölder maps.

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Sylvain Delpech. "Modulus of continuity of the Mazur map between unit balls of Orlicz spaces and approximation by Hölder mappings." Illinois J. Math. 49 (1) 195 - 216, Spring 2005. https://doi.org/10.1215/ijm/1258138314

Information

Published: Spring 2005
First available in Project Euclid: 13 November 2009

zbMATH: 1084.41012
MathSciNet: MR2157375
Digital Object Identifier: 10.1215/ijm/1258138314

Subjects:
Primary: 46E30
Secondary: 41A30

Rights: Copyright © 2005 University of Illinois at Urbana-Champaign

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Vol.49 • No. 1 • Spring 2005
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