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Isometries of a Bergman-Privalov-Type Space on the Unit Ball

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  • Stevo Stević
  • Sei-Ichiro Ueki

Abstract

We introduce a new space consisting of all holomorphic functions on the unit ball such that , where , ( is the normalized Lebesgue volume measure on , and is a normalization constant, that is, ), and for . Some basic properties of this space are presented. Among other results we proved that with the metric is an -algebra with respect to pointwise addition and multiplication. We also prove that every linear isometry of into itself has the form for some such that and some which is a holomorphic self-map of satisfying a measure-preserving property with respect to the measure . As a consequence of this result we obtain a complete characterization of all linear bijective isometries of .

Suggested Citation

  • Stevo Stević & Sei-Ichiro Ueki, 2009. "Isometries of a Bergman-Privalov-Type Space on the Unit Ball," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-16, November.
    • Handle: RePEc:hin:jnddns:725860
    DOI: 10.1155/2009/725860
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