|
The Dolbeault complex in infinite dimensions II
Author(s):
László
Lempert
Journal:
J. Amer. Math. Soc.
12
(1999),
775-793.
MSC (1991):
Primary 32F20, 46G20
Posted:
April 13, 1999
Part I:
J. Amer. Math. Soc. 11 (1998), 485-520
MathSciNet review:
1665984
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the equation on a ball , and prove that it is solvable if is a Lipschitz continuous, closed -form.
References:
- [C]
- G. Coeuré, Les équations de Cauchy-Riemann sur un espace de Hilbert, manuscript.
- [DGZ]
- R. Deville, G. Godefroy, V. Zizler, Smoothness and renormings in Banach spaces, Longman Scientific & Technical, Essex, England, 1993. MR 94d:46012
- [D]
- S. Dineen, Complex Analysis in Locally Convex Spaces, North Holland, Amsterdam, 1981. MR 84b:46050
- [GL]
- H. Grauert, I. Lieb, Das Ramirezsche Integral und die Lösung der Gleichung
im Bereiche der beschränkten Formen, Proc. Conf. Complex Analysis, 1969, Rice University, Rice University Studies 56 (1970), 29-50. MR 42:7938 - [H]
- G.M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb. 82 (1970), 300-308; English translation, Math. USSR Sb. 11 (1970), 273-281. MR 42:534
- [Ho]
- L. Hörmander, An Introduction to Complex Analysis in Several Variables, 3rd edition, North Holland, Amsterdam, 1990. MR 91a:32001
- [K]
- J. Kurzweil, On approximations in real Banach spaces, Studia Math. 14 (1954), 214-231. MR 16:932g
- [L]
- L. Lempert, The Dolbeault complex in infinite dimensions I, J. Amer. Math. Soc. 11 (1998), 485-520. CMP 98:13
- [M]
- P. Mazet, Analytic Sets in Locally Convex Spaces, North Holland, Amsterdam, 1984. MR 86i:32012
- [R]
- P. Raboin, Le problème du
sur un espace de Hilbert, Bull. Soc. Math. Fr. 107 (1979), 225-240. MR 80i:32052 - [Ry]
- R.A. Ryan, Holomorphic mappings in
, Trans. Amer. Math. Soc. 302 (1987), 797-811. MR 88h:46089
Similar Articles:
Retrieve articles in Journal of the American Mathematical Society
with
MSC (1991):
32F20, 46G20
Retrieve articles in all Journals with
MSC (1991):
32F20, 46G20
Additional Information:
László
Lempert
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907--1395
Email:
lempert@math.purdue.edu
DOI:
10.1090/S0894-0347-99-00296-9
PII:
S 0894-0347(99)00296-9
Keywords:
$\overline{\partial }$ equation,
Banach spaces
Received by editor(s):
September 22, 1998
Posted:
April 13, 1999
Additional Notes:
This research was partially supported by an NSF grant.
Copyright of article:
Copyright
1999,
American Mathematical Society
|