The Angular Distribution of Mass by Weighted Bergman Functions Distribución Angular de Masa mediante Funciones de Bergman con Peso
نویسندگان
چکیده
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 Aα 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 functions belonging to the unweighted Bergman space. We also prove that a such extension for α negative fails.
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