| Title:
|
The $\bar\partial$-Neumann operator and commutators of the Bergman projection and multiplication operators (English) |
| Author:
|
Haslinger, Friedrich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1247-1256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that compactness of the canonical solution operator to $\bar \partial $ restricted to $(0,1)$-forms with holomorphic coefficients is equivalent to compactness of the commutator $[\mathcal P,\bar M]$ defined on the whole $L^2_{(0,1)}(\Omega ),$ where $\bar M$ is the multiplication by $\bar z$ and $\mathcal P $ is the orthogonal projection of $L^2_{(0,1)}(\Omega )$ to the subspace of $(0,1)$ forms with holomorphic coefficients. Further we derive a formula for the $\bar \partial $-Neumann operator restricted to $(0,1)$ forms with holomorphic coefficients expressed by commutators of the Bergman projection and the multiplications operators by $z $ and $\bar z$. (English) |
| Keyword:
|
$\bar{\partial}$-equation |
| Keyword:
|
$\bar{\partial}$-Neumann operator |
| Keyword:
|
compactness |
| MSC:
|
32A36 |
| MSC:
|
32W05 |
| idZBL:
|
Zbl 1174.32015 |
| idMR:
|
MR2471181 |
| . |
| Date available:
|
2010-07-21T08:18:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140455 |
| . |
| Reference:
|
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