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Smooth Boundary Values Along Totally Real Submanifolds

Published online by Cambridge University Press:  20 November 2018

Edgar Lee Stout
Edgar Lee Stout*
Affiliation:
University of Washington, Seattle, Washington
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The main result of this paper is the following regularity result:

THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.

Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 2 , 01 April 1984 , pp. 240 - 248
Copyright
Copyright © Canadian Mathematical Society 1984

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