Uniform Convexity and Associate Spaces - UTU Research Portal

A1 Refereed original research article in a scientific journal

Uniform Convexity and Associate Spaces

Authors: Petteri Harjulehto, Peter Hästö

Publisher: Springer New York LLC

Publication year: 2018

Journal: Czechoslovak Mathematical Journal

Journal name in source: Czechoslovak Mathematical Journal

Volume: 68

Issue: 4

First page : 1011

Last page: 1020

Number of pages: 10

ISSN: 0011-4642

eISSN: 1572-9141

DOI: https://doi.org/10.21136/CMJ.2018.0054-17

Abstract

We prove that the associate space of a generalized Orlicz space L^ϕ(·) 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 L^ϕ(·) is uniformly convex if ϕ and ϕ* are weakly doubling.