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Siberian Mathematical Journal

, Volume 46, Issue 6, pp 969–994 | Cite as

The Cauchy Transform of Continuous Linear Functionals and Projections on the Weighted Spaces of Analytic Functions

  • O. E. Antonenkova
  • F. A. Shamoyan
Article

Abstract

Under some general assumptions on weight, we give a complete characterization of the Cauchy transform of continuous linear functionals on the weighted spaces of holomorphic functions in a ball. We construct an integral projection that sends the weighted spaces of measurable and n-harmonic functions in the ball onto the corresponding spaces of holomorphic functions.

Keywords

linear functional Cauchy transform weighted space holomorphic function 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • O. E. Antonenkova
    • 1
  • F. A. Shamoyan
    • 1
  1. 1.Bryansk State UniversityBryanskRussia

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