## Illinois Journal of Mathematics

### Modulus of continuity of the Mazur map between unit balls of Orlicz spaces and approximation by Hölder mappings

Sylvain Delpech

#### 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.

#### Article information

Source
Illinois J. Math., Volume 49, Number 1 (2005), 195-216.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138314

Digital Object Identifier
doi:10.1215/ijm/1258138314

Mathematical Reviews number (MathSciNet)
MR2157375

Zentralblatt MATH identifier
1084.41012

#### Citation

Delpech, Sylvain. Modulus of continuity of the Mazur map between unit balls of Orlicz spaces and approximation by Hölder mappings. Illinois J. Math. 49 (2005), no. 1, 195--216. doi:10.1215/ijm/1258138314. https://projecteuclid.org/euclid.ijm/1258138314