Abstract
In this survey a brief review of results on the Bergman kernel and Bergman distance concentrating on those fields of complex analysis which remain in the focus of the research interest of the authors is presented. The topics discussed contain general discussion of Lh spaces, behavior of the Bergman distance, regularity of extension of proper holomorphic mappings, and recent development in the theory of Bergman distance stemming from the pluripotential theory and very short discussion of the Lu Qi Keng problem. Ł. Kosinski • W. Zwonek ( ) Faculty of Mathematics and Computer Science, Department of Mathematics, Jagiellonian University, Krakow, Poland e-mail: lukasz.kosinski@im.uj.edu.pl; wlodzimierz.zwonek@im.uj.edu.pl © Springer Basel 2015 D. Alpay (ed.), Operator Theory, DOI 10.1007/978-3-0348-0667-1_68 73 74 Ł. Kosinski and W. Zwonek
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