Uniform Convexity and Associate Spaces




Petteri Harjulehto, Peter Hästö

PublisherSpringer New York LLC

2018

Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal

68

4

1011

1020

10

0011-4642

1572-9141

DOIhttps://doi.org/10.21136/CMJ.2018.0054-17



We prove that the associate space of a generalized Orlicz space Lϕ(·) is given by the conjugate modular ϕ* even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling Φ-function is equivalent to a doubling Φ-function. As a consequence, we conclude that Lϕ(·) is uniformly convex if ϕ and ϕ* are weakly doubling.



Last updated on 2024-26-11 at 17:17