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Journal Articles Bulletin des Sciences Mathématiques Year : 2019

Havin-Mazya type uniqueness theorem for Dirichlet spaces

Abstract

Let $\mu$ be a positive finite Borel measure on the unit circle. The associated Dirichlet space $\mathcal{D}(\mu)$ consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against the Poisson integral of $\mu$. We give a sufficient condition on a Borel subset $E$ of the unit circle which ensures that $E$ is a uniqueness set for $\mathcal{D}(\mu)$. {We also give somes examples of positive Borel measures $\mu$ and uniqueness sets for $\mathcal{D}(\mu)$.}
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Dates and versions

hal-01376878 , version 1 (05-10-2016)
hal-01376878 , version 2 (18-12-2019)

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Hafid Bahajji-El Idrissi, Omar El-Fallah, Karim Kellay. Havin-Mazya type uniqueness theorem for Dirichlet spaces. Bulletin des Sciences Mathématiques, inPress. ⟨hal-01376878v2⟩

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