21 feb 2019 -- 16:00
Aula D'Antoni, Roma Tor Vergata
Seminario di Analisi Complessa, nell’'aV
Abstract.
Carleson measures were introduced by Carleson in his celebrated solution of the corona problem; since then they have become an interesting subject of study on their own, mainly because they can be characterised in many different ways, both analytic and geometrical. In this talk we shall apply Carleson measures to the study of mapping properties of Toeplitz operators between weighted Bergman spaces on strongly pseudo convex domains. More precisely, if $T^\beta_\mu$ is the Toeplitz operator associated to the measure $\mu$ and having as kernel the Bergman kernel of the weighted Bergman space $A^2_\beta$, then (if $\beta$ is large enough) $T^\beta_\mu$ maps $A^{p_1}_{\alpha_1}$ into $A^{p_2}_{\alpha_2}$ if and only if $\mu$ is a Carleson measure of a suitable exponent. (Joint work with S. Mongodi and J. Raissy).