Carleson Measures and Reproducing Kernel Thesis in Dirichlet-type spaces

Gerardo Chacòn, Emmanuel Fricain, Mahmood Shabankhah

Published 2010-09-09, updated 2012-02-17Version 3

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.