The Duren–Carleson Theorem in Tube Domains over Symmetric Cones

Abstract

In the setting of tube domains over symmetric cones, we determine a necessary and sufficient condition on a Borel measure \(\mu \) so that the Hardy space \(H^{p}, 1\le p < \infty ,\) continuously embeds in the weighted Lebesgue space \(L^q (T_\Omega ,d\mu )\) with a larger exponent. Finally we use this result to characterize multipliers from \(H^{2m}\) to Bergman spaces for every positive integer m.