On Dirichlet spaces with a class of superharmonic weights

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Bao, Guanlong and Göğüş, Nihat Gökhan and Pouliasis, Stamatis (2018) On Dirichlet spaces with a class of superharmonic weights. Canadian Journal of Mathematics, 70 (4). pp. 721-741. ISSN 0008-414X (Print) 1496-4279 (Online)

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Abstract

In this paper, we investigate Dirichlet spaces D-mu with superharmonic weights induced by positive Borel measures mu on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for D-mu spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces H-mu(2) via the balayage of the measure mu. We show that D-mu is equal to H-mu(2) if and only if mu is a Carleson measure for D-mu. As an application, we obtain the reproducing kernel of D-mu when mu is an infinite sum of point-mass measures. We consider the boundary behavior and inner-outer factorization of functions in D-mu. We also characterize the boundedness and compactness of composition operators on D-mu.
Item Type: Article
Uncontrolled Keywords: Dirichlet space; Hardy space; superharmonic weight
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Nihat Gökhan Göğüş
Date Deposited: 25 Mar 2019 10:30
Last Modified: 26 Apr 2022 10:02
URI: https://research.sabanciuniv.edu/id/eprint/36899

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