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) |
Persistent link: | http://urn.fi/urn:nbn:fi-fe2019032610018 |
Language: | English |
Published: |
Institute of Mathematics, Czech Academy of Sciences,
2018
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Publish Date: | 2019-03-26 |
Description: |
AbstractWe 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. see all
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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 |
OADOI: | https://oadoi.org/10.21136/CMJ.2018.0054-17 |
Type of Publication: |
A1 Journal article – refereed |
Field of Science: |
111 Mathematics |
Subjects: | |
Copyright information: |
© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018. The original publication is available at https://articles.math.cas.cz/10.21136/CMJ.2018.0054-17 |