| Title:
|
The $L^2$ $\bar \partial $-Cauchy problem on weakly $q$-pseudoconvex domains in Stein manifolds (English) |
| Author:
|
Saber, Sayed |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
739-745 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a Stein manifold of complex dimension $n\ge 2$ and $\Omega \Subset X$ be a relatively compact domain with $C^2$ smooth boundary in $X$. Assume that $\Omega $ is a weakly \mbox {$q$-pseudoconvex} domain in $X$. The purpose of this paper is to establish sufficient conditions for the closed range of $\bar \partial $ on $\Omega $. Moreover, we study the \mbox {$\bar \partial $-problem} on $\Omega $. Specifically, we use the modified weight function method to study the weighted \mbox {$\bar \partial $-problem} with exact support in $\Omega $. Our method relies on the \mbox {$L^2$-estimates} by Hörmander (1965) and by Kohn (1973). (English) |
| Keyword:
|
$\bar \partial $ operator |
| Keyword:
|
$\bar \partial $-Neumann operator |
| Keyword:
|
$q$-convex domain |
| Keyword:
|
Stein manifold |
| MSC:
|
32F10 |
| MSC:
|
32W05 |
| idZBL:
|
Zbl 06537689 |
| idMR:
|
MR3407602 |
| DOI:
|
10.1007/s10587-015-0205-2 |
| . |
| Date available:
|
2015-10-04T18:13:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144440 |
| . |
| 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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| . |
