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Proceedings of the American Mathematical Society

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

 

 

Small sets of infinite type are benign for the $ \overline\partial$-Neumann problem


Author: Harold P. Boas
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943086-2
Keywords: $ \bar \partial $-Neumann problem, Bergman projection, global regularity
Article copyright: © Copyright 1988 American Mathematical Society