| Title:
|
A sharp form of an embedding into multiple exponential spaces (English) |
| Author:
|
Černý, Robert |
| Author:
|
Mašková, Silvie |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
751-782 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Omega $ be a bounded open set in $\mathbb R^n$, $n \geq 2$. In a well-known paper {\it Indiana Univ. Math. J.}, 20, 1077--1092 (1971) Moser found the smallest value of $K$ such that $$ \sup \bigg \{\int _{\Omega } \exp \Big (\Big (\frac {\left |f(x)\right |}K\Big )^{n/(n-1)}\Big )\colon f\in W^{1,n}_0(\Omega ),\|\nabla f\|_{L^n}\leq 1\bigg \}<\infty . $$ We extend this result to the situation in which the underlying space $L^n$ is replaced by the generalized Zygmund space $L^n\log ^{n-1}L \log ^{\alpha }\log L$ $(\alpha <n-1)$, the corresponding space of exponential growth then being given by a Young function which behaves like $\exp (\exp (t^{n/(n-1-\alpha )}))$ for large $t$. We also discuss the case of an embedding into triple and other multiple exponential cases. (English) |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
Orlicz-Sobolev spaces |
| Keyword:
|
embedding theorems |
| Keyword:
|
sharp constants |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 1224.46064 |
| idMR:
|
MR2672414 |
| . |
| Date available:
|
2010-07-20T17:17:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140603 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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