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Complete weights andv-peak points of spaces of weighted holomorphic functions

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Abstract

We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n,C n,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.

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Authors and Affiliations

  1. Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland

    Christopher Boyd

  2. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, 46100 Burjasot, Valencia, Spain

    Pilar Rueda

Authors
  1. Christopher Boyd
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  2. Pilar Rueda
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Additional information

The second author was supported by MCYT and FEDER Project BFM2002-01423.

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Boyd, C., Rueda, P. Complete weights andv-peak points of spaces of weighted holomorphic functions. Isr. J. Math. 155, 57–80 (2006). https://doi.org/10.1007/BF02773948

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  • DOI: https://doi.org/10.1007/BF02773948

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