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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $ H\sp 2$ corona problem and $ \overline\partial\sb b$ in weakly pseudoconvex domains


Author: Mats Andersson
Journal: Trans. Amer. Math. Soc. 342 (1994), 241-255
MSC: Primary 32F15; Secondary 32F05, 32F20, 46J15
MathSciNet review: 1145727
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Abstract: We derive a Bochner-Kodaira-Nakano-Morrey-Kohn-Hörmander type equality in holomorphic vector bundles and obtain $ {L^2}$-estimates for $ {\bar \partial _b}$ in a pseudoconvex domain that admits a plurisubharmonic $ {C^2}$ defining function. We combine these with the trick in Wolff's proof of the corona theorem and obtain a $ {H^2}$-corona theorem in such a domain.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1145727-3
PII: S 0002-9947(1994)1145727-3
Keywords: Corona theorem, $ {\bar \partial _b}$-equation
Article copyright: © Copyright 1994 American Mathematical Society