| Title:
|
Pointwise inequalities of logarithmic type in Hardy-Hölder spaces (English) |
| Author:
|
Chaabane, Slim |
| Author:
|
Feki, Imed |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
351-363 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove some optimal logarithmic estimates in the Hardy space ${H}^{\infty }(G)$ with Hölder regularity, where $G$ is the open unit disk or an annular domain of $\mathbb {C}$. These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space $H^{k,\infty }$ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem for the Laplace operator and the Robin inverse problem. (English) |
| Keyword:
|
Hardy-Sobolev space |
| Keyword:
|
Hardy-Landau-Littlewood inequality |
| Keyword:
|
Hölder regularity |
| Keyword:
|
Cauchy problem |
| Keyword:
|
inverse problem |
| Keyword:
|
logarithmic estimate |
| MSC:
|
30C40 |
| MSC:
|
30H05 |
| MSC:
|
30H10 |
| idZBL:
|
Zbl 06391499 |
| idMR:
|
MR3277741 |
| DOI:
|
10.1007/s10587-014-0106-9 |
| . |
| Date available:
|
2014-11-10T09:34:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144003 |
| . |
| Reference:
|
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