| Title:
|
On a class of $\overline{\partial}$-equations without solutions (English) |
| Author:
|
Hatziafratis, Telemachos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
503-509 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we construct $\overline{\partial }$-equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions. (English) |
| Keyword:
|
$\overline{\partial }$-equation |
| Keyword:
|
Bochner-Martinelli type kernels |
| MSC:
|
32A25 |
| MSC:
|
32F20 |
| MSC:
|
32W05 |
| idZBL:
|
Zbl 0970.32004 |
| idMR:
|
MR1666762 |
| . |
| Date available:
|
2009-01-08T18:45:46Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119028 |
| . |
| Reference:
|
[1] Aizenberg I., Yuzhakov A.: Integral representations in multidimensional complex analysis.Trans. Math. Monos., vol. 58, Amer. Math. Soc., Providence, R.I., 1983. MR 0735793 |
| Reference:
|
[2] Gunning R.: Introduction to Holomorphic Functions of Several Variables.Vol. III, Wadsworth and Brooks/Cole, 1990. Zbl 0699.32001, MR 1059457 |
| Reference:
|
[3] Hatziafratis T.: Integral representation formulas on analytic varieties.Pacific J. Math. 123 (1986), 71-91. Zbl 0591.32003, MR 0834139 |
| Reference:
|
[4] Henkin G.M., Leiterer J.: Andreotti-Grauert Theory by Integral Formulas.Birkhauser, 1988. Zbl 0654.32002, MR 0986248 |
| Reference:
|
[5] Kytmanov A.: The Bochner-Martinelli Integral and its Applications.Birkhauser, 1995. Zbl 0834.32001, MR 1409816 |
| Reference:
|
[6] Rudin W.: Function Theory in the Unit Ball of $\Bbb C^n$.Springer-Verlag, 1980. MR 0601594 |
| . |
