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Transactions of the American Mathematical Society

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



The Bergman projection on Hartogs domains in $ {\bf C}\sp 2$

Authors: Harold P. Boas and Emil J. Straube
Journal: Trans. Amer. Math. Soc. 331 (1992), 529-540
MSC: Primary 32H10; Secondary 32F15
MathSciNet review: 1062188
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Abstract: Estimates in $ {L^2}$ Sobolev norms are proved for the Bergman projection in certain smooth bounded Hartogs domains in $ {{\mathbf{C}}^2}$. In particular, (1) if the domain is pseudoconvex and "nonwormlike" (the normal vector does not wind on a critical set in the boundary), then the Bergman projection is regular; and (2) Barrett's counterexample domains with irregular Bergman projection nevertheless admit a priori estimates.

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Keywords: Bergman projection, $ \overline \partial $-Neumann operator, Hartogs domain, worm domain, a priori estimate
Article copyright: © Copyright 1992 American Mathematical Society