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Search: All articles in the CJM digital archive with keyword Dirichlet space

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1. CJM Online first

Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis
On Dirichlet spaces with a class of superharmonic weights
In this paper, we investigate Dirichlet spaces $\mathcal{D}_\mu$ with superharmonic weights induced by positive Borel measures $\mu$ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for $\mathcal{D}_\mu$ 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 $\mathcal{D}_\mu$ is equal to $H_{\mu}^{2}$ if and only if $\mu$ is a Carleson measure for $\mathcal{D}_\mu$. As an application, we obtain the reproducing kernel of $\mathcal{D}_\mu$ when $\mu$ is an infinite sum of point mass measures. We consider the boundary behavior and inner-outer factorization of functions in $\mathcal{D}_\mu$. We also characterize the boundedness and compactness of composition operators on $\mathcal{D}_\mu$.

Keywords:Dirichlet space, Hardy space, superharmonic weight
Categories:30H10, 31C25, 46E15

2. CJM 2010 (vol 62 pp. 961)

Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan
Multiplicative Isometries and Isometric Zero-Divisors
For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisors
Categories:30H05, 46E15

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