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arXiv · 1601.04899

The Duren-Carleson theorem in tube domains over symmetric cones

David Békollé·Benoît F. Sehba·Edgar L. Tchoundja
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Abstract

In the setting of tube domains over symmetric cones, $T_\Omega$, we study the characterization of the positive Borel measures $\mu$ for which the Hardy space $H^p$ is continuously embedded into the Lebesgue space $L^q (T_\Omega, d\mu)$, $0<p<q<\infty.$ Extending a result due to Blasco for the unit disc, we reduce the problem to standard measures. We obtain that a Hardy space $H^{p}$, $1\leq p < \infty,$ embeds continuously in weighted Bergman spaces with larger exponents. Finally we use this result to characterize multipliers from $H^{2m}$ to Bergman spaces for every positive integer $m$.

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David Békollé, Benoît F. Sehba, Edgar L. Tchoundja. 2016-01-19. The Duren-Carleson theorem in tube domains over symmetric cones. https://arxiv.org/abs/1601.04899

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