Author:
Bao Guanlong,Göğüş Nihat Gokhan,Pouliasis Stamatis
Abstract
AbstractIn this paper, we investigate Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces via the balayage of the measure μ. We show that is equal to if and only if μ is a Carleson measure for . As an application, we obtain the reproducing kernel of when μ is an infinite sum of point-mass measures. We consider the boundary behavior and innerouter factorization of functions in . We also characterize the boundedness and compactness of composition operators on .
Publisher
Canadian Mathematical Society
Cited by
7 articles.
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