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On Weights Which Admit Reproducing Kernel of Szegő Type

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Abstract

In this paper we generalize the concept of the Szegö kernel by putting the weight of integration in the definition of the inner product in the Szegö space. We give some sufficient conditions for the weight in order for the Szegö kernel of the correspoding space to exist. We give examples of weights on unit ball for which there is no Szegö kernel of the corresponding Szegö space. Then using biholomorphisms we prove that there exist such weights for a large class of domains. At the end we show that weighted Szegö kernel depends continuously in some sense on weight of integration.

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Authors and Affiliations

  1. Warsaw University of Technology, Warsaw, Poland

    T. Ł. Żynda

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  1. T. Ł. Żynda
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Correspondence to T. Ł. Żynda.

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Żynda, T.Ł. On Weights Which Admit Reproducing Kernel of Szegő Type. J. Contemp. Mathemat. Anal. 55, 320–327 (2020). https://doi.org/10.3103/S1068362320050064

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  • DOI: https://doi.org/10.3103/S1068362320050064

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