Uniform convexity and associate spaces
Harjulehto, Petteri; Hästö, Peter (2018-04-13)
Harjulehto, Petteri
Hästö, Peter
Institute of Mathematics
13.04.2018
Harjulehto, P. & Hästö, P. Czech Math J (2018) 68: 1011. https://doi.org/10.21136/CMJ.2018.0054-17
https://rightsstatements.org/vocab/InC/1.0/
© 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
https://rightsstatements.org/vocab/InC/1.0/
© 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
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2019032610018
https://urn.fi/URN:NBN:fi-fe2019032610018
Tiivistelmä
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.
Kokoelmat
- Avoin saatavuus [31941]