Kernel estimate and capacity in the Dirichlet spaces
Language
en
Article de revue
This item was published in
Journal of Functional Analysis. 2019, vol. 276, n° 3, p. 867–895.
Elsevier
English Abstract
We study the capacity in the sense of Beurling-Deny associated with the Dirichlet space $\mathcal{D}(\mu)$ where $\mu$ is a finite positive Borel measure on the unit circle. First, we obtain a sharp asymptotic estimate ...Read more >
We study the capacity in the sense of Beurling-Deny associated with the Dirichlet space $\mathcal{D}(\mu)$ where $\mu$ is a finite positive Borel measure on the unit circle. First, we obtain a sharp asymptotic estimate of the norm of the reproducing kernel of $\mathcal{D}(\mu)$. It allows us to give an estimates of the capacity of points and arcs of the unit circle. We also provide a new conditions on closed sets to be polar. Our method is based on sharp estimates of norms of some outer functions which allow us to transfer these problems to an estimate of the reproducing kernel of an appropriate weighted Sobolev space.Read less <
Origin
Hal imported