| Title:
|
On a higher-order Hardy inequality (English) |
| Author:
|
Edmunds, David E. |
| Author:
|
Rákosník, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
124 |
| Issue:
|
2 |
| Year:
|
1999 |
| Pages:
|
113-121 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Hardy inequality $\int_\Omega|u(x)|^pd(x)^{-p}\dd x\le c\int_\Omega|\nabla u(x)|^p\dd x$ with $d(x)=\operatorname{dist}(x,\partial\Omega)$ holds for $u\in C^\infty_0(\Omega)$ if $\Omega\subset\Bbb R^n$ is an open set with a sufficiently smooth boundary and if $1<p<\infty$. P. Hajlasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for $p=1$. (English) |
| Keyword:
|
Hardy inequality |
| Keyword:
|
capacity |
| Keyword:
|
maximal function |
| Keyword:
|
Sobolev space |
| Keyword:
|
$p$-thick set |
| MSC:
|
26D10 |
| MSC:
|
31C15 |
| MSC:
|
42B25 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 0936.31010 |
| idMR:
|
MR1780685 |
| DOI:
|
10.21136/MB.1999.126250 |
| . |
| Date available:
|
2009-09-24T21:36:01Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126250 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
