Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds

Mattia Calzi and Marco M. Peloso

Mathematische Nachrichten, 2023, vol. 296, issue 10, 4854-4887

Abstract: In this paper, we introduce and study Carleson and sampling measures on Bernstein spaces on a class of quadratic CR manifold called Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to the given Siegel CR manifold are Lp$L^p$‐integrable with respect to a natural measure. For these spaces, we prove necessary and sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.

Date: 2023
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https://doi.org/10.1002/mana.202200058

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