On consequences of certain boundary conditions on the unit circle

Title:

On consequences of certain boundary conditions on the unit circle

Creator:

Adamczyk, Gabriela

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:28b816d4-77e1-47a3-af89-363cc6469b9b
uuid:28b816d4-77e1-47a3-af89-363cc6469b9b
doi:10.21136/MB.2000.125955

Subject:

bounded holomorphic functions, Carathéodory functions, harmonic measure, and extreme points

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let P denote the well-known class of Caratheodory functions of the form p(z) = 1+ciz-i , z e A = {z ∈ ℂ: \z\ < 1}, with positive real part in the unit disc and let H(M) stand for the class of holomorphic functions commonly bounded by M in A. In 1992, J. Fuka and Z. J. Jakubowski began an investigation of families of mappings p ∈ P fulfilling certain additional boundary conditions on the unit circle T. At first, the authors examined the class P(B, b; α) of functions defined by conditions given by the upper limits for two disjoint open arcs of T. After that, such boundary conditions given, in particular, by the nontangential limits, were assumed for different subsets of the unit circle. In parallel, G. Adamczyk started to search for properties of families, contained in H(M) and satisfying certain similar conditions on T. The present article belongs to the above series of papers. In the first section we will consider subclasses of V of functions satisfying some inequalities on several arcs of T, whereas in Sections 2 and 3-families of mappings f ∈ H(M) with conditions given for measurable subsets of the unit circle T.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

173-186

Source:

Mathematica bohemica | 2000 Volume:125 | Number:2

Harvested from:

CDK

Metadata only:

false