On the zeros of functions in Bergman spaces and in some other related classes of functions |
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Authors: | Daniel Girela,M. Auxiliadora Má rquez |
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Affiliation: | Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain |
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Abstract: | A well-known theorem of H.S. Shapiro and A.L. Shields implies that if f?0 is a function which belongs to the Bergman space Ap (0<p<∞) and {zk} is a sequence of zeros of f which is contained in a Stolz angle, then {zk} satisfies the Blaschke condition. In this paper we improve this result. We consider a large class of regions contained in the unit disc D which touch ∂D at a point ξ tangentially and we prove that the mentioned result remains true if we substitute a Stolz angle by any of these regions of tangential approach. |
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Keywords: | Sequence of zeros Blaschke condition Tangential approach region Bergman spaces |
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