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.
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Original Russian Text Copyright © 2005 Antonenkova O. E. and Shamoyan F. A.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 1208–1234, November–December, 2005.
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Antonenkova, O.E., Shamoyan, F.A. The Cauchy Transform of Continuous Linear Functionals and Projections on the Weighted Spaces of Analytic Functions. Sib Math J 46, 969–994 (2005). https://doi.org/10.1007/s11202-005-0094-y
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DOI: https://doi.org/10.1007/s11202-005-0094-y