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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The Dolbeault complex in infinite dimensions II


Author: László Lempert
Journal: J. Amer. Math. Soc. 12 (1999), 775-793
MSC (1991): Primary 32F20, 46G20
Published electronically: April 13, 1999
Part I: J. Amer. Math. Soc. (1998), 485-520
MathSciNet review: 1665984
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Abstract: We study the equation $\overline{\partial }u=f$ on a ball $B(R)\subset l^{1}$, and prove that it is solvable if $f$ is a Lipschitz continuous, closed $(0,1)$-form.


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Additional Information

László Lempert
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907–1395
Email: lempert@math.purdue.edu

DOI: http://dx.doi.org/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
Published electronically: April 13, 1999
Additional Notes: This research was partially supported by an NSF grant.
Article copyright: © Copyright 1999 American Mathematical Society