Uniform Convexity and Associate Spaces
: Petteri Harjulehto, Peter Hästö
Publisher: Springer New York LLC
: 2018
: Czechoslovak Mathematical Journal
: Czechoslovak Mathematical Journal
: 68
: 4
: 1011
: 1020
: 10
: 0011-4642
: 1572-9141
DOI: https://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.