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.
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Békollé, D., Sehba, B.F. & Tchoundja, E.L. The Duren–Carleson Theorem in Tube Domains over Symmetric Cones. Integr. Equ. Oper. Theory 86, 475–494 (2016). https://doi.org/10.1007/s00020-016-2336-8
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DOI: https://doi.org/10.1007/s00020-016-2336-8