Generalizations of the higher dimensional Suita conjecture and its\n relation with a problem of Wiegerinck

2018/11/07 by Włodzimierz Zwonek, Zbigniew Błocki, Zwonek, Wlodzimierz +1 · 3 citations
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1811.02977

Abstract

We generalize the inequality being a counterpart of the several complex\nvariables version of the Suita conjecture. For this aim higher order\ngeneralizations of the Bergman kernel are introduced. As a corollary some new\npartial results on the dimension of the Bergman space in pseudoconvex domains\nare given. A relation between the problem of Wiegerinck on possible dimension\nof the Bergman space of unbounded pseudoconvex domains in general case and in\nthe case of balanced domains is also shown. Moreover, some classes of domains\nwhere the answer to the problem of Wiegerinck is positive are given.\nAdditionally, regularity properties of functions involving the volumes of\nAzukawa indicatrices are shown.\n

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• Subharmonic variation of Azukawa pseudometrics for balanced domains
• On the p-Bergman kernel with respect to a functional ξ
• On the dimension of the p-Bergman spaces

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