Holomorphic function spaces on homogeneous Siegel domains

Calzi, Mattia; Peloso, Marco M.

doi:10.4064/dm833-3-2021

Cited by 8 publications

(113 citation statements)

References 58 publications

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“…Clearly, there is a dimensional constant N ∈ N such that the fibres of ι have at most N elements. Therefore, using [7,Lemma 3.25] and Proposition 3.7, we see that there is a dimensional constant C > 0 such that (f (ζ j , z j )) j ℓ p (J ) there is a sequence (ζ j , x j ) j of elements of N such that L (ζj ,xj+iΦ(ζj )) µ converges vaguely to µ ′ . Hence,…”

Section: Sampling Measuresmentioning

confidence: 91%

“…for every j ∈ J. For every j ∈ J, take a sequence (x j,j ′ ) j ′ ∈N of elements of F which is a finite union of separated families, 7 and assume that…”

Section: Sampling Measuresmentioning

confidence: 99%

“…6 It suffices to take a family (ζ j , x j ) j of elements of Supp µ ′ which is maximal for the relation d((ζ j , x j ), (ζ k , x k )) 2R. 7 We say that a family…”

Section: Sampling Measuresmentioning

confidence: 99%

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Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Calzi¹,

Peloso²

2022

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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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Section: Sampling Measuresmentioning

confidence: 91%

“…for every j ∈ J. For every j ∈ J, take a sequence (x j,j ′ ) j ′ ∈N of elements of F which is a finite union of separated families, 7 and assume that…”

Section: Sampling Measuresmentioning

confidence: 99%

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Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Calzi¹,

Peloso²

2022

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“…One of the main questions in the theory of holomorphic function spaces is the boundedness of projection operators. In this setting, it is known the operator P s induces a continuous endomorphism of L p,q s (C + ) if and only if 2s > s see, e.g., [18,Proposition 5.20 and Corollary 5.27]. 1 We also define an associated 'positive' operator by…”

Section: Introductionmentioning

confidence: 99%

Boundedness of Bergman projectors on homogeneous Siegel domains

Calzi,

Peloso

2022

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In this paper we study the boundedness of Bergman projectors on weighted Bergman spaces on homogeneous Siegel domains of Type II. As it appeared to be a natural approach in the special case of tube domains over irreducible symmetric cones, we study such boundedness on the scale of mixed-norm weighted Lebesgue spaces. The sharp range for the boundedness of such operators is essentially known only in the case of tube domains over Lorentz cones.In this paper we prove that the boundedness of such Bergman projectors is equivalent to variuos notions of atomic decomposition, duality, and characterization of boundary values of the mixed-norm weighted Bergman spaces, extending results moslty known only in the case of tube domains over irreducible symmetric cones. Some of our results are new even in the latter simpler context.We also study the simpler, but still quite interesting, case of the "positive" Bergman projectors, the integral operator in which the Bergman kernel is replaced by its absolute value. We provide a useful characterization which was previously known for tube domains. s = {0} if s < 0, and also if s = 0 and q < ∞. In addition, A p,∞ 0 is the classical Hardy space H p (C + ). In order to avoid trivialities, from now on we shall assume s > 0. In addition, for simplicity, in this introductory section we shall generally limit ourselves to the case p, q 1. Then, the

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“…We mention [ARS08, ARS10, AL18], [FX15], [RS16] and references therein. The Drury-Arveson on the Siegel upper half-space U has been studied in [ARS10] and [AMPS19], see also [CP20] for some properties on other unbounded domains.…”

Section: Introductionmentioning

confidence: 99%

The Drury--Arveson space on the Siegel upper half-space and a von Neumann type inequality

Arcozzi

Chalmoukis

Monguzzi

et al. 2021

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In this work we study what we call Siegel-dissipative vector of commuting operators pA 1 , . . . , A d`1 q on a Hilbert space H and we obtain a von Neumann type inequality which involves the Drury-Arveson space DA on the Siegel upper half-space U. The operator A d`1 is allowed to be unbounded and it is the infinitesimal generator of a contraction semigroup te ´iτ A d`1 u τ ă0 . We then study the operator e ´iτ A d`1 A α where A α " A α1 1 ¨¨¨A α d d for α P N d and prove that can be studied by means of model operators on a weighted L 2 space. To prove our results we obtain a Paley-Wiener type theorem for DA and we investigate some multiplier operators on DA as well.In the case d " 0 Drury's result reduces to the classical von Neumann Inequality ([vN51]) and the multiplier operator norm on H 2 pDq takes the place of } ¨}MpDApB d`1 qq . Namely, given a Hilbert

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Holomorphic function spaces on homogeneous Siegel domains

Cited by 8 publications

References 58 publications

Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Carleson and Sampling measures on Bernstein spaces on Siegel CR Manifolds

Boundedness of Bergman projectors on homogeneous Siegel domains

The Drury--Arveson space on the Siegel upper half-space and a von Neumann type inequality

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