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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Small sets of infinite type are benign for the $\overline \partial$-Neumann problem
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by Harold P. Boas PDF
Proc. Amer. Math. Soc. 103 (1988), 569-578 Request permission

Abstract:

An explicit construction shows that the $\bar \partial$-Neumann operator and the Bergman and Szegő projections are globally regular in every smooth bounded pseudoconvex domain whose set of boundary points of infinite type has Hausdorff two-dimensional measure equal to zero. On the other hand there are examples of domains with globally regular $\bar \partial$-Neumann operator but whose infinite-type points fill out an open subset of the boundary.
References
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 569-578
  • MSC: Primary 32F20; Secondary 35N15
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0943086-2
  • MathSciNet review: 943086