Superlogarithmic Estimates on Pseudoconvex Domains and CR Manifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jul 2002Embargo end date: 01 Oct 2004Publisher:JSTORJournal:The Annals of Mathematics, volume 156, page 213 (issn: 0003-486X,

Copyright policy )Funded by:NSF | Partial Differential Equa...

Authors: Kohn, J. J.;

doi: 10.2307/3597189 , 10.48550/arxiv.math/0410353

arXiv: math/0410353

Superlogarithmic Estimates on Pseudoconvex Domains and CR Manifolds

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Abstract

This paper is concerned with proving superlogarithmic estimates for the operator $\Box_b$ on pseudoconvex CR manifolds and using them to establish hypoellipticity of $\Box_b$ and of the $\bar{\partial}$-Neumann problem. These estimates are established under the assumption that subellipticity degenerates in certain specified ways.

36 pages published version

Related Organizations

College of New Jersey
United States

Keywords

CR manifolds as boundaries of domains, Mathematics - Complex Variables, $\overline\partial_b$ and $\overline\partial_b$-Neumann operators, Hypoelliptic equations, hypoellipticity, FOS: Mathematics, Complex Variables (math.CV), $\square_b$ operator, superlogarithmic estimate, 32W10 (primary) 32V15, 32W05, 35H10, 35N15 (secondary)

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