Carleson measures for Hardy–Sobolev spaces

Tchoundja, Edgar

doi:10.1080/17476930802429149

Cited by 6 publications

(12 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On the other hand in [18,19] it is shown that K m (z, w) on B 2d is a Calderón-Zygmund operator with parameters m, τ = 1/2 with respect to the quasi-metric ∆. We remark that this is a non-trivial observation.…”

Section: Necessary and Sufficientmentioning

confidence: 70%

See 1 more Smart Citation

Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

Volberg¹,

Wick²

2012

ajm

View full text Add to dashboard Cite

The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman-type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov-Sobolev space of analytic functions B σ 2 on the complex ball of C d . In particular, we demonstrate that for any σ > 0, the Carleson measures for the space are characterized by a "T1 Condition". The method of proof of these results is an extension and another application of the work originated by Nazarov, Treil and the first author.

show abstract

Section: Necessary and Sufficientmentioning

confidence: 70%

“…It was proved by N. Arcozzi, R. Rochberg, and E. Sawyer using the machinery of function spaces on trees, see [2]. It was also proved, more in the spirit of what appears in this paper, by E. Tchoundja, see [18,19]. He adapted the proof of J. Verdera of the boundedness of the Cauchy operator on L 2 (µ), [24].…”

Section: Carleson Measures Onmentioning

confidence: 71%

Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

Volberg¹,

Wick²

2012

ajm

View full text Add to dashboard Cite

show abstract

“…Then, f is a DA(B d+1 )-multiplier if and only if f ∈ H ∞ (B d+1 ) and dν f is a Carleson measure for DA(B d+1 ). A few years later N. Arcozzi, R. Rochberg and E. Sawyer in [5] completely characterized the Carleson measures of DA(B d+1 ); see also [18,19,21]. Hence, the multiplier algebra of the Drury-Arveson space on the unit ball is completely characterized.…”

Section: Pointwise Multipliers On the Drury-arveson Spacementioning

confidence: 97%

The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality

Arcozzi

Chalmoukis

Monguzzi

et al. 2021

Integr. Equ. Oper. Theory

View full text Add to dashboard Cite

In this work we study what we call Siegel–dissipative vector of commuting operators $$(A_1,\ldots , A_{d+1})$$ ( A 1 , … , A d + 1 ) on a Hilbert space $${{\mathcal {H}}}$$ H and we obtain a von Neumann type inequality which involves the Drury–Arveson space DA on the Siegel upper half-space $${{\mathcal {U}}}$$ U . The operator $$A_{d+1}$$ A d + 1 is allowed to be unbounded and it is the infinitesimal generator of a contraction semigroup $$\{e^{-i\tau A_{d+1}}\}_{\tau <0}$$ { e - i τ A d + 1 } τ < 0 . We then study the operator $$e^{-i\tau A_{d+1}}A^{\alpha }$$ e - i τ A d + 1 A α where $$A^{\alpha }=A_1^{\alpha _1}\cdots A^{\alpha _d}_d$$ A α = A 1 α 1 ⋯ A d α d for $$\alpha \in {\mathbb N}_0^d$$ α ∈ N 0 d and prove that can be studied by means of model operators on a weighted $$L^2$$ 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.

show abstract

“…Then f is a DApB d`1 q-multiplier if and only if f P H 8 pB d`1 q and dν f is a Carleson measure for DApB d`1 q. A few years later N. Arcozzi, R. Rochberg and E. Sawyer completeley characterized in [ARS08] the Carleson measures of DApB d`1 q; see also [Tch08b,Tch08a], [VW12]. Hence, the multiplier algebra of the Drury-Arveson space on the unit ball is completely characterized.…”

Section: Pointwise Multipliers On the Drury-arveson Spacementioning

confidence: 99%

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

Arcozzi

Chalmoukis

Monguzzi

et al. 2021

Preprint

View full text Add to dashboard Cite

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

show abstract

Carleson measures for Hardy–Sobolev spaces

Cited by 6 publications

References 7 publications

Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality

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

Contact Info

Product

Resources

About