scholarly journals Toeplitz Algebras on Strongly Pseudoconvex Domains

2007 ◽  
Vol 185 ◽  
pp. 171-186 ◽  
Author(s):  
Guangfu Cao
Keyword(s):  
Continuous Function ◽  
Pseudoconvex Domain ◽  
Function Algebra ◽  
Pseudoconvex Domains ◽  
Chern Classes ◽  
Toeplitz Algebra ◽  
Cohomology Groups ◽  
Ring Isomorphism ◽  
Strongly Pseudoconvex Domains ◽  
Strongly Pseudoconvex Domain

AbstractIn the present paper, it is proved that theK0-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to theK0-group of the relative continuous function algebra, and is thus isomorphic to the topologicalK0-group of the boundary of the relative domain. Further there exists a ring isomorphism between theK0-groups of Toeplitz algebras and the Chern classes of the relative boundaries of strongly pseudoconvex domains. As applications of our main result,K-groups of Toeplitz algebras on some special strongly pseudoconvex domains are computed. Our results show that the Toeplitz algebras on strongly pseudoconvex domains have rich structures, which deeply depend on the topological structures of relative domains. In addition, the first cohomology groups of Toeplitz algebras are also computed.

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 .

Asymptotic Expansions of Invariant Metrics of Strictly Pseudoconvex Domains

1995 ◽  
Vol 38 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Siqi Fu
Keyword(s):  
Continuous Function ◽  
Asymptotic Expansions ◽  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Invariant Metrics ◽  
Kobayashi Metric ◽  
Signed Distance ◽  
Strictly Pseudoconvex Domain ◽  
Kobayashi Metrics

AbstractIn this paper we obtain the asymptotic expansions of the Carathéodory and Kobayashi metrics of strictly pseudoconvex domains with C∞ smooth boundaries in ℂn. The main result of this paper can be stated as following:Main Theorem. Let Ω be a strictly pseudoconvex domain with C∞ smooth boundary. Let FΩ(z,X) be either the Carathéodory or the Kobayashi metric of Ω. Let δ(z) be the signed distance from z to ∂Ω with δ(z) < 0 for z ∊ Ω and δ(z) ≥ 0 for z ∉ Ω. Then there exist a neighborhood U of ∂Ω, a constant C > 0, and a continuous function C(z,X):(U ∩ Ω) × ℂn -> ℝ such that and|C(z,X)| ≤ C|X| for z ∊ U ∩ Ω and X ∊ ℂn

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).

Hankel Operators on Pseudoconvex Domains of Finite Type in ℂ2

1998 ◽  
Vol 50 (3) ◽  
pp. 658-672 ◽  
Author(s):  
Frédéric Symesak
Keyword(s):  
Hardy Space ◽  
Finite Type ◽  
Pseudoconvex Domain ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Sufficient Condition ◽  
Schatten Class ◽  
Strictly Pseudoconvex Domain

AbstractThe aimof this paper is to study small Hankel operators h on the Hardy space or on weighted Bergman spaces,where Ω is a finite type domain in ℂ2 or a strictly pseudoconvex domain in ℂn. We give a sufficient condition on the symbol ƒ so that h belongs to the Schatten class Sp, 1 ≤ p < +∞.

scholarly journals On the existence of Kobayashi and Bergman metrics for Model domains

2020 ◽  
Author(s):  
Nikolay Shcherbina
Keyword(s):  
Entire Function ◽  
Continuous Function ◽  
Pseudoconvex Domain ◽  
Plurisubharmonic Function ◽  
Holomorphic Curves ◽  
List Type ◽  
Bergman Metric ◽  
The Core ◽  
Bounded Smooth ◽  
Bergman Metrics

Abstract We prove that for a pseudoconvex domain of the form $${\mathfrak {A}} = \{(z, w) \in {\mathbb {C}}^2 : v > F(z, u)\}$$ A = { ( z , w ) ∈ C 2 : v > F ( z , u ) } , where $$w = u + iv$$ w = u + i v and F is a continuous function on $${\mathbb {C}}_z \times {\mathbb {R}}_u$$ C z × R u , the following conditions are equivalent: The domain $$\mathfrak {A}$$ A is Kobayashi hyperbolic. The domain $$\mathfrak {A}$$ A is Brody hyperbolic. The domain $$\mathfrak {A}$$ A possesses a Bergman metric. The domain $$\mathfrak {A}$$ A possesses a bounded smooth strictly plurisubharmonic function, i.e. the core $$\mathfrak {c}(\mathfrak {A})$$ c ( A ) of $$\mathfrak {A}$$ A is empty. The graph $$\Gamma (F)$$ Γ ( F ) of F can not be represented as a foliation by holomorphic curves of a very special form, namely, as a foliation by translations of the graph $$\Gamma ({\mathcal H})$$ Γ ( H ) of just one entire function $${\mathcal {H}} : {\mathbb {C}}_z \rightarrow {\mathbb {C}}_w$$ H : C z → C w .

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