Linear dimension-free estimates in the embedding theorem for Schrödinger operators

Dragičević, Oliver; Volberg, Alexander

doi:10.1112/jlms/jdr036

Cited by 22 publications

(57 citation statements)

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“…Recently, Dragičevic and Volberg in a series of papers ( [11], [12], [13], and [14]) have developed another approach, different from any previous ones, where they use a technique involving Bellman functions. These Bellman functions allow them to obtain dimension free bilinear Littlewood-Paley estimates.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Dragičevic and Volberg have studied classical and Gaussian (Hermite polynomial) context in [11]. Riesz transforms associated with the harmonic oscillator and more general Schrödinger operators were analyzed in [12] and [14], respectively. In [13], bilinear Littlewood-Paley estimates related to elliptic operators were established.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…A fundamental ingredient for the proof of our main result is the Bellman function. A function introduced by Nazarov and Treil ( [30]) and some modifications of it have been used in different settings ( [7], [11], [12], [14], [43], and [44]). Assume that p ≥ 2.…”

Section: Proofs Of Theorems 11 and 12mentioning

confidence: 99%

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Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings

2020

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In this article we prove dimension free L p -boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the L p -norms for the Bessel-Riesz transforms in terms of p, establishing a linear behaviour with respect to p. We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator.2010 Mathematics Subject Classification. 42A50, 42B20, 42B25.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings

2020

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“…The origins of Q lie in the paper of F. Nazarov and S. Treil [68]. A modification of their function has been later applied by A. Volberg and the second author in [26,28].…”

Section: Bounded H ∞ -Calculus Via Nazarov-treil Bellman Functionmentioning

confidence: 99%

Bounded holomorphic functional calculus for nonsymmetric Ornstein-Uhlenbeck operators

Carbonaro¹,

Dragičević²

2019

Annali Scuola Normale Superiore - Classe Di Scienze

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We study bounded holomorphic functional calculus for nonsymmetric infinite dimensional Ornstein-Uhlenbeck operators L . We prove that if −L generates an analytic semigroup on L 2 (γ∞), then L has bounded holomorphic functional calculus on L r (γ∞), 1 < r < ∞, in any sector of angle ϑ > ϑ * r , where γ∞ is the associated invariant measure and ϑ * r the sectoriality angle of L on L r (γ∞). The angle ϑ * r is optimal. In particular our result applies to any nondegenerate finite dimensional Ornstein-Uhlenbeck operator, with dimension-free estimates.

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“…Since the seminal papers, the technique has been used in numerous settings: see e.g. [4,15,16,18,19] and references therein.…”

Section: Vol 78 (2014)mentioning

confidence: 99%

Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh–Fourier Series

Oşekowski

2013

Integr. Equ. Oper. Theory

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Abstract. Suppose that d ≥ 1 is an integer, α ∈ (0, d) is a fixed parameter and let Iα be the fractional integral operator associated with d-dimensional Walsh-Fourier series on [0, 1)d . The paper contains the proof of the sharp weak-type estimateThe proof rests on Bellman-function-type method: the above estimate is deduced from the existence of a certain family of special functions.Mathematics Subject Classification (2010). Primary 42B25, 42B30; Secondary 42B35.

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Linear dimension-free estimates in the embedding theorem for Schrödinger operators

Cited by 22 publications

References 0 publications

Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings

Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings

Bounded holomorphic functional calculus for nonsymmetric Ornstein-Uhlenbeck operators

Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh–Fourier Series

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