Carleson Measures and Reproducing Kernel Thesis in Dirichlet-type spaces.

Gerardo Chacòn (1) , Emmanuel Fricain (2) , Mahmood Shabankhah (3)

1 Departamento de Matematicas
2 ICJ - Institut Camille Jordan
3 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper, using a generalization of a Richter and Sundberg representation theorem, we give a new characterization of Carleson measures for the Dirichlet-type space $\mathcal D(\mu)$ when $\mu$ is a finite sum of point masses. A reproducing kernel thesis result is also established in this case.

Mots clés: Dirichlet-type spaces; Carleson measures; reproducing kernel thesis

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Gerardo Chacòn, Emmanuel Fricain, Mahmood Shabankhah. Carleson Measures and Reproducing Kernel Thesis in Dirichlet-type spaces.. St. Petersburg Mathematical Journal, 2013, 24 (6), pp.847-861. ⟨hal-00516302v3⟩