Points of monotonicity in F-normed Orlicz function spaces

In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function spaces equipped with a Mazur–Orlicz F -norm and generated by a monotone (non-convex in general) Orlicz function are studied. We show...

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Bibliographic Details
Published inAequationes mathematicae Vol. 97; no. 4; pp. 659 - 682
Main Authors Yang, Yabo, Cui, Yunan, Kaczmarek, Radosław
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2023
Springer Nature B.V
Subjects
Analysis
Combinatorics
Function space
Mathematics
Mathematics and Statistics
Theorems
Primary 46E30
Secondary 46A80
Orlicz space
Points of lower (upper) strict monotonicity
Mazur–Orlicz
norm
Points of lower (upper) local uniform monotonicity
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Summary:In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function spaces equipped with a Mazur–Orlicz F -norm and generated by a monotone (non-convex in general) Orlicz function are studied. We show that both the necessary and sufficient conditions and the suitable theorems are formulated in full generality. Moreover, lower (upper) strict monotonicity and lower (upper) local uniform monotonicity theorems of the paper https://doi.org/10.1007/s00010-018-0615-y are revealed as corollaries in this paper.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-023-00961-2