Harjulehto, P. & Hästö, P. Czech Math J (2018) 68: 1011. https://doi.org/10.21136/CMJ.2018.0054-17

### Uniform convexity and associate spaces

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Author: Harjulehto, Petteri1; Hästö, Peter1,2
Organizations: 1Department of Mathematics and Statistics, FI-20014 University of Turku, Turku, Finland
2Department of Mathematical Sciences, FI-90014 University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
Language: English
Published: Institute of Mathematics, Czech Academy of Sciences, 2018
Publish Date: 2019-03-26
Description:

# Abstract

We prove that the associate space of a generalized Orlicz space $$L^{\varphi(\cdot)}$$ is given by the conjugate modular $$\varphi^*$$ even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling $$\Phi$$-function is equivalent to a doubling $$\Phi$$-function. As a consequence, we conclude that $$L^{\varphi(\cdot)}$$ is uniformly convex if $$\varphi$$ and $$\varphi^*$$ are weakly doubling.

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Series: Czechoslovak mathematical journal
ISSN: 0011-4642
ISSN-E: 1572-9141
ISSN-L: 0011-4642
Volume: 68
Issue: 4
Pages: 1011 - 1020
DOI: 10.21136/CMJ.2018.0054-17