| Title:
|
Uniform convexity and associate spaces (English) |
| Author:
|
Harjulehto, Petteri |
| Author:
|
Hästö, Peter |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
1011-1020 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that the associate space of a generalized Orlicz space $L^{\phi (\cdot )}$ is given by the conjugate modular $\phi ^*$ 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 $L^{\phi (\cdot )}$ is uniformly convex if $\phi $ and $\phi ^*$ are weakly doubling. (English) |
| Keyword:
|
generalized Orlicz space |
| Keyword:
|
Musielak-Orlicz space |
| Keyword:
|
nonstandard growth |
| Keyword:
|
variable exponent |
| Keyword:
|
double phase |
| Keyword:
|
uniform convexity |
| Keyword:
|
associate space |
| MSC:
|
46A25 |
| MSC:
|
46E30 |
| idZBL:
|
Zbl 07031693 |
| idMR:
|
MR3881892 |
| DOI:
|
10.21136/CMJ.2018.0054-17 |
| . |
| Date available:
|
2018-12-07T06:19:45Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147517 |
| . |
| Reference:
|
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