Totally disconnected set non-removable for Lipschitz continous bounded analytic functions.

Totally Disconnected Julia Set for Different Classes of Meromorphic Functions

We study a class of functions A given by Epstein in Towers of finite type complex analytic maps, ProQuest LLC, Ann Arbor, MI, 1993, called finite-type maps. We extend a result related with the Julia set given by Baker, Domı́nguez in Some connectedness properties of Julia sets, Complex Variable Theory Appl. 41 (2000), 371–389, and Baker, Domı́nguez, and Herring in Dynamics of functions meromorphic...

Removable singularities for analytic functions in BMO and locally Lipschitz spaces

In this paper we study removable singularities for holomorphic functions such that supz∈Ω |f (z)|dist(z, ∂Ω) < ∞. Spaces of this type include spaces of holomorphic functions in Campanato classes, BMO and locally Lipschitz classes. Dolzhenko (1963), Král (1976) and Nguyen (1979) characterized removable singularities for some of these spaces. However, they used a different removability concept th...

A Non - Removable Set

Bounded Analytic Functions

If D is a domain in the complex s-plane, then the family B=B(D) of bounded analytic functions in D is defined as consisting of those analytic functions ƒ(z) which are regular and single-valued in D and which satisfy the inequality \f(z) | < 1 at all points of D. The classical investigations of the family B(D) were restricted to the case in which D is a simply-connected domain. In fact, D was ge...

On Bounded Analytic Functions

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [l] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a...