# 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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Cited literature [19 references]

https://hal.archives-ouvertes.fr/hal-01376878
Contributor : Karim Kellay <>
Submitted on : Wednesday, December 18, 2019 - 7:35:49 PM
Last modification on : Friday, December 20, 2019 - 1:44:30 AM
Long-term archiving on: : Thursday, March 19, 2020 - 9:25:36 PM

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### Identifiers

• HAL Id : hal-01376878, version 2
• ARXIV : 1912.09988

### Citation

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

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