Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 49, Number 1 (2005), 195-216.
Modulus of continuity of the Mazur map between unit balls of Orlicz spaces and approximation by Hölder mappings
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.
Illinois J. Math., Volume 49, Number 1 (2005), 195-216.
First available in Project Euclid: 13 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 41A30: Approximation by other special function classes
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