Zero-Sets of Continuous Holomorphic Functions on the Boundary of a Strongly Pseudoconvex Domain

1978 ◽  
Vol s2-18 (3) ◽  
pp. 484-488 ◽  
Author(s):  
Barnet M. Weinstock
Keyword(s):  
Pseudoconvex Domain ◽  
Holomorphic Functions ◽  
Zero Sets ◽  
Strongly Pseudoconvex Domain

scholarly journals A remark on the theorem of Ohsawa-Takegoshi

2000 ◽  
Vol 158 ◽  
pp. 185-189 ◽  
Author(s):  
Klas Diederich ◽  
Emmanuel Mazzilli
Keyword(s):  
Pseudoconvex Domain ◽  
Complex Analysis ◽  
Holomorphic Functions ◽  
Growth Conditions ◽  
Analytic Subset ◽  
Famous Theorem ◽  
Restriction Operator

If D ⊂ ℂn is a pseudoconvex domain and X ⊂ D a closed analytic subset, the famous theorem B of Cartan-Serre asserts, that the restriction operator r : (D) → (X) mapping each function F to its restriction F|X is surjective. A very important question of modern complex analysis is to ask what happens to this result if certain growth conditions for the holomorphic functions on D and on X are added.

Smooth Boundary Values Along Totally Real Submanifolds

1984 ◽  
Vol 36 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Edgar Lee Stout
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Regularity Result ◽  
Boundary Values ◽  
Real Submanifolds ◽  
Strongly Pseudoconvex Domain ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Class C ◽  
Totally Real

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).

scholarly journals On the Distribution of Zero Sets of Holomorphic Functions: II

2019 ◽  
Vol 53 (1) ◽  
pp. 65-68 ◽  
Author(s):  
B. N. Khabibullin ◽  
E. B. Menshikova
Keyword(s):  
Holomorphic Functions ◽  
Zero Sets

scholarly journals Admissible limits of bloch functions on bounded strongly pseudoconvex domains

1996 ◽  
Vol 54 (1) ◽  
pp. 1-3
Author(s):  
Hu Zhangjian
Keyword(s):  
Pseudoconvex Domain ◽  
Bloch Function ◽  
Pseudoconvex Domains ◽  
Bloch Functions ◽  
Radial Limits ◽  
Strongly Pseudoconvex Domains ◽  
Almost Everywhere ◽  
Strongly Pseudoconvex Domain ◽  
Almost All

Let be a bounded strongly pseudoconvex domain with C2 boundary . In this paper we prove that for a Bloch function in the existance of radial limits at almost all implies the existence of admissible limits almost everywhere on .

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