Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 92795, 12 pages
doi:10.1155/JIA/2006/92795

Boundary behaviour of analytic functions in spaces of Dirichlet type

Daniel Girela1 and José Ángel Peláez2

 1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, Málaga 29071, Spain
2Departamento de Matemática Aplicada, Escuela Politécnica, Universidad de Málaga, Campus de El Ejido, Málaga 29071, Spain
Received 24 June 2005; Revised 11 October 2005; Accepted 8 November 2005

Abstract

For 0<p<∞ and α>−1, we let 𝒟αp be the space of all analytic functions f in D={z∈ℂ:|z|<1} such that f' belongs to the weighted Bergman space Aαp. We obtain a number of sharp results concerning the existence of tangential limits for functions in the spaces 𝒟αp. We also study the size of the exceptional set E(f)={eiθ∈∂D:V(f,θ)=∞}, where V(f,θ) denotes the radial variation of f along the radius [0,eiθ), for functions f∈𝒟αp.