Abstract
In this paper, we investigate Dirichlet spaces Dμ with superharmonic weights induced by positive Borel measures μ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for Dμ spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces H2 via the balayage of the measure μ. We show that Dμ is equal to H2 if and only if μ is a Carleson measure for Dμ. As an application, we obtain the reproducing kernel of Dμ when μ is an infinite sum of point-mass measures. We consider the boundary behavior and inner-outer factorization of functions in Dμ. We also characterize the boundedness and compactness of composition operators on Dμ.
Original language | English |
---|---|
Pages (from-to) | 721-741 |
Number of pages | 21 |
Journal | Canadian Journal of Mathematics |
Volume | 70 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2018 |
Keywords
- Dirichlet space
- Hardy space
- Superharmonic weight