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 sketch the solution of this problem in dimension one, that is the case of Hardy space on the upper half plane, given by L. Carleson (1962) for $p = q$, and $P$. Duren (1969) for $p < q$. I will also report on recent advances on this problem based on joint work with D. Bekolle and B. Sehba.
Carleson measure Problem for Hardy spaces on tube domains over symmetric cones
Speaker:
Edgar Tchoundja
Institution:
University of Yaoundé I
Schedule:
Thursday, March 1, 2018 - 14:00
Location:
Luigi Stasi Seminar Room, ICTP
Abstract:
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