| Title:
|
Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains (English) |
| Author:
|
Çelik, Mehmet |
| Author:
|
Zeytuncu, Yunus E. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
207-217 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
On complete pseudoconvex Reinhardt domains in $\mathbb {C}^2$, we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in $\mathbb {C}^2$ that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator $H_{\bar {z}_1 \bar {z}_2}$ is Hilbert-Schmidt. (English) |
| Keyword:
|
canonical solution operator for $\overline {\partial }$-problem |
| Keyword:
|
Hankel operator |
| Keyword:
|
Hilbert-Schmidt operator |
| MSC:
|
32A36 |
| MSC:
|
47B10 |
| MSC:
|
47B35 |
| idZBL:
|
Zbl 06738513 |
| idMR:
|
MR3633007 |
| DOI:
|
10.21136/CMJ.2017.0471-15 |
| . |
| Date available:
|
2017-03-13T12:09:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146049 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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