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

Stevo Stević and Sei-Ichiro Ueki

Discrete Dynamics in Nature and Society, 2009, vol. 2009, 1-16

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 .

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:725860

DOI: 10.1155/2009/725860

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