Abstract
In this paper, we deal with superharmonically weighted Dirichlet spaces \(\mathcal {D}_{\omega }\). First, we prove that the classical Dirichlet space is the largest, among all these spaces, which contains no infinite Blaschke product. Next, we give new sufficient conditions on a Blaschke sequence to be a zero set for \(\mathcal {D}_{\omega }\). Our conditions improve Shapiro-Shields condition for \(\mathcal {D}_{\alpha }\), when α ∈ (0,1).
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Idrissi, H.BE., El-Fallah, O. Blaschke Products and Zero Sets in Weighted Dirichlet Spaces. Potential Anal 53, 1299–1316 (2020). https://doi.org/10.1007/s11118-019-09807-6
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DOI: https://doi.org/10.1007/s11118-019-09807-6