Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

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 $L^p$-integrable with respect to a natural measure. For these spaces, we prove necessary and sufficients conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.

24 pages, no figures

References in corpus (3)

• Carleson and reverse Carleson measures on homogeneous Siegel domains
• Bernstein Spaces on Siegel CR Manifolds
• Sampling in spaces of entire functions of exponential type in ${\mathbb{C}}^{n+1}$

Cited by in corpus (2)

• Paley-Wiener-Schwartz Theorems on Quadratic CR Manifolds
• On the Theory of Bergman Spaces on Homogeneous Siegel Domains