Havin-Mazya type uniqueness theorem for Dirichlet spaces
Language
en
Article de revue
This item was published in
Bulletin des Sciences Mathématiques. 2019
Elsevier
Date
2019English 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 ...Read more >
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 $\mathcal{D}(\mu)$.}Read less <
English Keywords
uniqueness set
weighted Dirichlet spaces
capacity
Origin
Hal imported