Jouni Rättyä
Professor of mathematics at the University of Eastern Finland.
Title: Carleson measures for Bergman spaces
Abstract:
A positive Borel measure $\mu$ on the unit disc is called the $q$-Carleson measure for the Bergman space $A^p_\omega$ if the idenity mapping from $A^p_\omega$ to the Lebesgue space $L^q_\mu$ is bounded. In this talk we give an overview of these measures in the case when $\omega$ is a radial doubling weight in the unit disc and show a number of applications of these measures. At the end of the talk we pose a few open problems related to the less understood case of non-radial weights.