This article is cited in 10 papers

The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions

O. E. Antonenkova, F. A. Shamoyan

I. G. Petrovsky Bryansk State University

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.

UDC: 517.55

Received: 13.07.2004

 English version: Siberian Mathematical Journal, 2005, 46:6, 969–994

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