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Multipliers on Pseudoconvex Domains with Real Analytic Boundaries

Joseph J. Kohn — 2010

Bollettino dell'Unione Matematica Italiana

This paper is concerned with (weakly) pseudoconvex real analytic hypersurfaces in 𝐂 n . We are motivated by the study of local boundary regularity of the ¯ -Neumann problem. Subelliptic estimates in a neighborhood of a point P in the boundary (which imply regularity) are controlled by ideals of germs of real analytic functions I 1 ( P ) , , I n - 1 ( P ) . These ideals have the property that a subelliptic estimate holds for ( p , q ) -forms in a neighborhood of P if and only if 1 I q ( P ) . The geometrical meaning of this is that 1 I q ( P ) if and only...

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