| Title:
|
Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces (English) |
| Author:
|
Černý, Robert |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
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1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
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557-571 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $n\geq 2$ and $\Omega\subset \mathbb R^n$ be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space $W_0L^{\Phi}(\Omega)$, where the Young function $\Phi$ behaves like $t^n\log^{\alpha}(t)$, $\alpha<n-1$, for $t$ large, into the Zygmund space $Z_0^{\frac{n-1-\alpha}{n}}(\Omega)$. We also study the same problem for the embedding of the generalized Lorentz-Sobolev space $W_0^mL^{\frac{n}{m},q}\log^{\alpha}L(\Omega)$, $m< n$, $q\in (1,\infty]$, $\alpha<\frac{1}{q'}$, embedded into the Zygmund space $Z_0^{\frac{1}{q'}-\alpha}(\Omega)$. (English) |
| Keyword:
|
Orlicz-Sobolev spaces |
| Keyword:
|
Lorentz-Sobolev spaces |
| Keyword:
|
Trudinger embedding |
| Keyword:
|
Moser-Trudinger inequality |
| Keyword:
|
best constants |
| MSC:
|
26D10 |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idMR:
|
MR3016426 |
| . |
| Date available:
|
2013-03-02T13:40:49Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143190 |
| . |
| Reference:
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