Complex interpolation between two weighted Bergman spaces on tubes over symmetric cones

Békollè, David; Gonessa, Jocelyn; Nana, Cyrille

doi:10.1016/s1631-073x(03)00257-7

Cited by 4 publications

(9 citation statements)

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“…Theorem 4.5 shows that (1) implies ( 2), (4 ′ ), and (5). In addition, (2) is equivalent to (3) thanks to [18, Proposition 5.21], while (5) clearly implies (6). By means of Theorem 4.5, we also see that (3) implies (1).…”

Section: Induces An Antilinear Isomorphism Ofmentioning

confidence: 53%

“…Proposition 4.1 and [18, Lemma 5.15]). In order to conclude, it then suffices to prove that both (4) and (4 ′ ) imply (6). Arguing as in the proof of Proposition 4.6 and using [18,Theorem 3.22], this is easily established.…”

Section: Induces An Antilinear Isomorphism Ofmentioning

confidence: 88%

“…In Section 5, we shall consider how complex interpolation interacts with the preceding properties, thus extending some results of [6]. In Section 6 we shall prove some transference results between weighted Bergman spaces on a Siegel domain of type II and the corresponding tube domain, thus extending some results of [8].…”

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confidence: 87%

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Boundedness of Bergman projectors on homogeneous Siegel domains

Calzi,

Peloso

2022

Preprint

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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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Section: Induces An Antilinear Isomorphism Ofmentioning

confidence: 53%

Section: Induces An Antilinear Isomorphism Ofmentioning

confidence: 88%

See 1 more Smart Citation

Boundedness of Bergman projectors on homogeneous Siegel domains

Calzi,

Peloso

2022

Preprint

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“…In Sect. 5, we shall consider how complex interpolation interacts with the preceding properties, thus extending some results of [6]. In particular, we shall prove that the set of (p, q, s, s) for which the (equivalent) properties ( 1)-( 4) hold is convex.…”

Section: Introductionmentioning

confidence: 69%

“…Remark 2. 6 The second part of Proposition 2.5 is actually [18, (2) of Proposition 5.18], which, in turn, extends [3,Proposition 4.34]. The argument which leads to the proof of these results is based on the interplay between modulation 'in space' and traslation 'in frequency' when using the (Euclidean) Fourier transform.…”

Section: An Extension Operatormentioning

confidence: 76%

Boundedness of Bergman projectors on homogeneous Siegel domains

Calzi

Peloso

2022

Rend. Circ. Mat. Palermo, II. Ser

View full text Add to dashboard Cite

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 mostly 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 modulus. We provide a useful characterization which was previously known for tube domains.

show abstract