One-box conditions for Carleson measures for the Dirichlet space - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2015

One-box conditions for Carleson measures for the Dirichlet space

Omar El-Fallah
  • Fonction : Auteur
  • PersonId : 849735
Karim Kellay

Résumé

We give a simple proof of the fact that a finite measure $\mu$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $\mu(S(I))=O(\phi(|I|))$, where $\phi: (0, 2 ] \to (0,1)$ is an increasing function such that \[ \int_{0}^{2\pi}(\phi (x)/x) dx < \infty/ \] We further show that the integral condition on $\phi$ is sharp.
Fichier non déposé

Dates et versions

hal-00835052 , version 1 (18-06-2013)

Identifiants

  • HAL Id : hal-00835052 , version 1

Citer

Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford. One-box conditions for Carleson measures for the Dirichlet space. Proceedings of the American Mathematical Society, 2015, 143 (2), pp.679-684. ⟨hal-00835052⟩

Collections

CNRS IMB INSMI
105 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More