Superlogarithmic estimates on pseudoconvex domains and CR manifolds

2004/10/15 by J. J. Kohn
Mathematics · #math.CV #msc:32W10 #msc:32V15 #msc:32W05 #msc:35H10 #msc:35N15

paper · pdf

published as Ann. of Math. (2), Vol. 155 (2002), no. 1, 213--348 · 36 pages published version

arxiv created 2004/10/15 · arxiv updated 2009/12/01

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 ∂-Neumann problem. These estimates are established under the assumption that subellipticity degenerates in certain specified ways.

Related

• Subellipticity of the ∂-Neumann problem on a weakly q-pseudoconvex/concave domain
• Regularity of the ∂-Neumann problem by means of superlogarithmic multipliers
• Local regularity of the Green operator in a CR manifold of general "type"
• Subelliptic and Maximal L^p Estimates for the Complex Green Operator on non-pseudoconvex domains
• Monotonicity of Subelliptic Estimates on Rigid Pseudoconvex Domains