Analysis Seminar: "On Carleson Measures for Hardy Spaces on Tube Domains over Symmetric Cones"

Edgar Tchoundja

Abstract:  Let $\Omega$ be a symmetric cone in $\mathbb R^n$ and $T_\Omega=\mathbb R^n+i\Omega$, the tube domain over $\Omega$. Let $H^p(T_\Omega)$ be the Hardy space on $T_\Omega$ which is a higher dimension generalization of the classical Hardy space on the upper half plane. We consider the Carleson measure problem for Hardy space on $T_\Omega$. That is the problem of characterizing positive measures $\mu$ in $T_\Omega$ such that  $H^p(T_\Omega)$ continuously imbedded into $L^q(T_\Omega,\mu)$. In this talk, I will report on recent advances on this problem based on joint work with D. Bekolle and  B. Sehba.

 

Organizer: John McCarthy