Uniform convexity, reflexivity, superreflexivity and B convexity of generalized Sobolev spaces W^1,Φ

Authors

Anna Kamińska, University of MemphisFollow
Mariusz Żyluk

Abstract

We investigate Sobolev spaces W1,Φ associated to Musielak-Orlicz spaces LΦ. We first present conditions for the boundedness of the Voltera operator in LΦ. Employing this, we provide necessary and sufficient conditions for W1,Φ to contain isomorphic subspaces to ℓ∞ or ℓ1. Further we give necessary and sufficient conditions in terms of the function Φ or its complementary function Φ⁎ for reflexivity, uniform convexity, B-convexity and superreflexivity of W1,Φ. As corollaries we obtain the corresponding results for Orlicz-Sobolev spaces W1,φ where φ is an Orlicz function, the variable exponent Sobolev spaces W1,p(⋅) and the Sobolev spaces associated to double phase functionals.

Publication Title

Journal of Mathematical Analysis and Applications

Recommended Citation

Kamińska, A., & Żyluk, M. (2022). Uniform convexity, reflexivity, superreflexivity and B convexity of generalized Sobolev spaces W^1,Φ. Journal of Mathematical Analysis and Applications, 509 (1) https://doi.org/10.1016/j.jmaa.2021.125925