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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The $H^ 2$ corona problem and $\overline \partial _ b$ in weakly pseudoconvex domains
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by Mats Andersson PDF
Trans. Amer. Math. Soc. 342 (1994), 241-255 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 342 (1994), 241-255
  • MSC: Primary 32F15; Secondary 32F05, 32F20, 46J15
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1145727-3
  • MathSciNet review: 1145727