Further properties of the Bergman spaces of slice regular functions

2014/06/19 by Fabrizio Colombo, Colombo, Fabrizio, J. Oscar Gonzalez-Cervantes +3 · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1406.5210

to appear in Advances in Geometry

arxiv created 2014/06/19 · arxiv updated 2014/06/23

Abstract

In this paper we continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paper we mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitable weights are taken into account. Finally, we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.

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