Uniform Convexity and Associate Spaces

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 conc...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2018-12, Vol.68 (4), p.1011-1020
Main Authors: Harjulehto, Petteri, Hästö, Peter
Format: Article
Language:English
Subjects:
Analysis
Convex and Discrete Geometry
Convexity
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Orlicz space
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Summary: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.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2018.0054-17