Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
MathSciNet review: 943086
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32F20, 35N15

Retrieve articles in all journals with MSC: 32F20, 35N15

Additional Information

PII: S 0002-9939(1988)0943086-2
Keywords: $ \bar \partial $-Neumann problem, Bergman projection, global regularity
Article copyright: © Copyright 1988 American Mathematical Society