Locally univalent functions, VMOA and the Dirichlet space

Bounded Analytic Functions in the Dirichlet Space

In this paper we study the Hilbert space of analytic functions with finite Dirichlet integral in a connected open set C2 in the complex plane. We show that every such function can be represented as a quotient of two bounded analytic functions, each of which has a finite Dirichlet integral. This has several consequences for the structure of invariant subspaces of the algebra of multiplication op...

Classical Families of Univalent Functions in the Hornich Space

In this paper the simple structure between some convex sets in the Banach space H introduced by Hornich is used to determine the extreme points of the families K(a) of convex functions of order ~ and V(k) of functions with bounded boundary rotation k ~. For close-to-convex functions of order {1,/3 ~ ]0, 1[, a partial result is given. The results for K(~) and V(k) agree with those that hold for ...

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Univalent Functions with Univalent Derivatives. Ii

Convex and Starlike Univalent Functions