scholarly journals Decomposition of the Laplacian and pluriharmonic Bloch functions

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 97-102
Author(s):  
Ern Kwon
Keyword(s):  
Bloch Function ◽  
Bloch Functions ◽  
Complex Ball

We decompose the invariant Laplacian of the deleted unit complex ball by two directional Laplacians, tangential one and radial one. We give a characterization of pluriharmonic Bloch function in terms of the growth of these Laplacians.

Interpolating sequences for the derivatives of Bloch functions

1992 ◽  
Vol 34 (1) ◽  
pp. 35-41 ◽  
Author(s):  
K. R. M. Attele
Keyword(s):  
Bergman Space ◽  
Hankel Operator ◽  
Essential Norm ◽  
Bloch Function ◽  
Sufficient Condition ◽  
Bloch Functions ◽  
Interpolating Sequences ◽  
Analytic Symbol ◽  
Derivatives Of

AbstractWe prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .

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 .

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

A Real Characterization of the Pre-Dual of Bloch Functions

1983 ◽  
Vol s2-27 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Geraldo Soares de Souza ◽  
G. Sampson
Keyword(s):  
Bloch Functions

scholarly journals A CHARACTERIZATION OF BLOCH FUNCTIONS

2006 ◽  
Vol 21 (2) ◽  
pp. 287-292 ◽  
Author(s):  
Ern-Gun Kwon ◽  
Ok-Hee Shim ◽  
Eun-Kyu Bae
Keyword(s):  
Bloch Functions

Generalized Bloch Mappings in Complex Hilbert Space

1977 ◽  
Vol 29 (2) ◽  
pp. 299-306 ◽  
Author(s):  
Fletcher D. Wicker
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bloch Function ◽  
Complex Hilbert Space ◽  
Function Concept ◽  
Bounded Analytic Functions ◽  
Bloch Functions ◽  
Normal Functions ◽  
The Family

Anderson, Clunie and Pommerenke defined and studied the family of Bloch functions on the unit disc (see [1]). This family strictly contains the space of bounded analytic functions. However, all Bloch functions are normal and therefore enjoy the “nice” properties of normal functions. The importance of the Bloch function concept is the combination of their richness as a family and their “nice” behavior.

ON THE HOLLAND–WALSH CHARACTERIZATION OF BLOCH FUNCTIONS

2008 ◽  
Vol 51 (2) ◽  
pp. 439-441 ◽  
Author(s):  
Miroslav Pavlović
Keyword(s):  
Unit Ball ◽  
Bloch Functions

AbstractIt is proved that the Bloch norm of an arbitrary $C^1$-function defined on the unit ball $\mathbb{B}_n\subset\mathbb{R}^n$ is equal to$$ \sup_{x,y\in\mathbb{B}_n,\,x\neq y}{(1-|x|^2)^{1/2}(1-|y|^2)^{1/2}}\frac{|f(x)-f(y)|}{|x-y|}. $$

Additive Automorphic Functions and Bloch Functions

1994 ◽  
Vol 46 (3) ◽  
pp. 474-484
Author(s):  
Rauno Aulaskari ◽  
Peter Lappan
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Fuchsian Group ◽  
Bloch Function ◽  
Hyperbolic Distance ◽  
Finitely Generated ◽  
Bloch Functions ◽  
The Right ◽  
Uniformly Continuous ◽  
Automorphic Functions

AbstractA function f analytic in the unit disk D is said to be strongly uniformly continuous hyperbolically, or SUCH, on a set E ⊂ D if for each ∊ > 0 there exists a δ > 0 such that |f(z) — f(z')| < ∊ whenever z and z' are points in E and the hyperbolic distance between z and z' is less than δ. We show that f is a Bloch function in D if and only if |f| is SUCH in D. A function f is said to be additive automorphic in D relative to a Fuchsian group F if, for each γ ∊ Γ, there exists a constant Aγ such that f(γ(z)) =f(z) + Aγ. We show that if an analytic function f is additive automorphic in D relative to a Fuchsian group Γ, where Γ is either finitely generated or if the fundamental region F of Γ has the right kind of structure, and if |f| is SUCH in F, then f is a Bloch function. We show by example that some restrictions on Γ are needed.

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