Geodesic
Smooth Boundary Values Along Totally Real Submanifolds
Canadian journal of mathematics, Tome 36 (1984) no. 2, pp. 240-248

Voir la notice de l'article provenant de la source Cambridge University Press

The main result of this paper is the following regularity result:THEOREM. Let D ⊂ C N be 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 C r − 0, and if Σ is of class Ck, then fΣ is of class C k − 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). 
Stout, Edgar Lee. Smooth Boundary Values Along Totally Real Submanifolds. Canadian journal of mathematics, Tome 36 (1984) no. 2, pp. 240-248. doi: 10.4153/CJM-1984-015-9
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