The Angular Distribution of Mass by Weighted Bergman Functions Distribución Angular de Masa mediante

Let D be the open unit disk in the complex plane. For ε> 0 we consider the sector Σε = {z ∈ C: | arg z | < ε}. We prove that for every α ≥ 0 and for each ε> 0 there is a constant K> 0 depending only on α and ε such that for any function f in the weighted Bergman space A1α univalent on D, and f(0) = 0, then∫ f−1(Σε) |f(z)|dAα(z)> K‖f‖1,α. This result extends a theorem of Marshall and Smith in [MS] for func-tions belonging to the unweighted Bergman space. We also prove that a such extension for α negative fails. Key words and phrases: Bergman space, univalent functions, har-monic measure, hyperbolic metric. Resumen Sea D el disco unitario en el plano complejo. Sea ε> 0 y conside-remos el sector Σε = {z ∈ C: | arg z | < ε}. Probaremos que para cada α ≥ 0 y para cada ε> 0 existe una constante K> 0, que depende sól