Carleson and Reverse Carleson Measures on Homogeneous Siegel Domains

Calzi, Mattia; Peloso, Marco M.

doi:10.1007/s11785-021-01177-5

Cited by 12 publications

(14 citation statements)

References 36 publications

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“…For some general facts on quadratic CR manifolds see [5,32], and for a recent account of analysis on Siegel Type II domain see [16,17,18]. Fourier analysis on N plays a relevant role in the study of various function spaces of holomorphic functions on D, and in this work.…”

Section: Statement Of the Main Resultsmentioning

confidence: 99%

Bernstein Spaces on Siegel CR Manifolds

Calzi¹,

Peloso²

2021

Preprint

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In this paper we introduce and study Bernstein spaces on a class of quadratic CR manifolds, which we call Siegel CR manifolds. These are spaces of entire functions of exponential type whose restrictions to a given Siegel CR submanifold are L p -integrable with respect to a natural measure. For these spaces, among other results, we prove the Plancherel-Pólya inequality, a Bernstein inequality and a sufficient condition for a sequence to be sampling. √ 2π f 0 induces an isometric isomorphism of B 2 κ onto L 2 ([−κ, κ]).

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Section: Statement Of the Main Resultsmentioning

confidence: 99%

Bernstein Spaces on Siegel CR Manifolds

Calzi¹,

Peloso²

2021

Preprint

Self Cite

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“…We now provide an abstract, yet quite powerful, sufficient condition for sampling measures, based on [26, Theorem 5] (cf. also [8,Theorem 7.9]). We shall then draw several corollaries.…”

Section: Sampling Measuresmentioning

confidence: 98%

“…This result in inspired by [23,Theorem 4.2] (cf. also [8,Theorem 7.6]). The proof is different, though.…”

Section: Sampling Measuresmentioning

confidence: 98%

Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Calzi¹,

Peloso²

2022

Preprint

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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. (ζ, x) • (ζ ′ , z ′ ) := (ζ + ζ ′ , x + iΦ(ζ) + z ′ + 2iΦ(ζ ′ , ζ))

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“…We may also derive somewhat analogous, yet less precise, necessary conditions for sampling measures using standard techniques (cf. e.g., [8,26]). See Proposition 5.6.…”

Section: Introductionmentioning

confidence: 99%

Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds

Calzi

Peloso

2023

Mathematische Nachrichten

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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 sufficient conditions for a Radon measure to be a Carleson or a sampling measure. We also provide sufficient conditions for sampling sequences.

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Carleson and Reverse Carleson Measures on Homogeneous Siegel Domains

Cited by 12 publications

References 36 publications

Bernstein Spaces on Siegel CR Manifolds

Bernstein Spaces on Siegel CR Manifolds

Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Carleson and sampling measures on Bernstein spaces on Siegel CR manifolds

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