Bibliographic Details
| Title: |
Compactness of the canonical solution operator of \(\bar\partial\) on bounded pseudoconvex domains |
| Authors: |
Knirsch, Wolfgang |
| Publisher Information: |
Wiley (Wiley-VCH), Weinheim |
| Subject Terms: |
Bergman spaces of functions in several complex variables, Toeplitz operators, Hankel operators, Wiener-Hopf operators, d-bar equation, Bergman-Toeplitz operators, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, \(\overline\partial\)-Neumann operator, canonical solution operator, \((0,q)\)-forms with holomorphic coefficients |
| Description: |
The main result of this paper is an explicit formula for the canonical solution operator \(S_{q+1}\) to \(\overline{\partial} \) restricted to \((0,q)\)-forms with holomorphic coefficients. The restriction to forms with holomorphic coefficients is essential for the proof and it shows an interesting relationship of \(\overline{\partial} \) to the Bergman kernel and certain multiplication operators. In the second part the explicit formula for the solution operator to \(\overline{\partial} \) is applied to generalize a result of \textit{N. Salinas}, \textit{A. Sheu} and \textit{H. Upmeier} [Ann. Math. (2) 130, 531--565 (1989; Zbl 0708.47021)], concerning compactness of the solution operator, the \(\overline{\partial} \)- Neumann operator and certain Bergman-Toeplitz operators. |
| Document Type: |
Article |
| File Description: |
application/xml |
| DOI: |
10.1002/1522-2616(200211)245:1<94::aid-mana94>3.0.co;2-h |
| Access URL: |
https://zbmath.org/1848362 |
| Accession Number: |
edsair.c2b0b933574d..6d21c153c354d2d2581a48dc12bcc20e |
| Database: |
OpenAIRE |