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. 721741. ISSN 0008414X (Print) 14964279 (Online)
This is the latest version of this item.
Official URL: http://dx.doi.org/10.4153/CJM20170051
Abstract
In this paper, we investigate Dirichlet spaces Dmu with superharmonic weights induced by positive Borel measures mu on the open unit disk. We establish the AlexanderTaylorUllman inequality for Dmu spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces Hmu(2) via the balayage of the measure mu. We show that Dmu is equal to Hmu(2) if and only if mu is a Carleson measure for Dmu. As an application, we obtain the reproducing kernel of Dmu when mu is an infinite sum of pointmass measures. We consider the boundary behavior and innerouter factorization of functions in Dmu. We also characterize the boundedness and compactness of composition operators on Dmu.
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 
Available Versions of this Item

On Dirichlet spaces with a class of superharmonic weights. (deposited 23 Aug 2017 14:36)
 On Dirichlet spaces with a class of superharmonic weights. (deposited 25 Mar 2019 10:30) [Currently Displayed]