Stein’s Square Function $$G_\alpha $$ G α and Sparse Operators

Carro, María Jesús Casals; Domingo-Salazar, Carlos

doi:10.1007/s12220-016-9733-8

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…where As it is wellknown, many authors and even in the last years have studied Bochner-Riesz means in R n and maximal and square functions associated with them ( [5,11,16,21,36,44,48] and [71]). We recall that the critical exponent for the Bochner-Riesz means in R n is α = n−1 2 .…”

Section: Introductionmentioning

confidence: 99%

“…The square function g λ ψ λ,α is a Bessel version of the Stein square function introduced in [67]. Quantitative weighted L p -inequalities for the classical Stein square function were obtained in [16]. In [17] Chen, Duong and Yan established L p -boundedness properties for Stein square function associated with operators in spaces of homogeneous type.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative weighted estimates for Harmonic analysis operators in the Bessel setting by using sparse domination

2022

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In this paper we obtain quantitative weighted $$L^p$$ L p -inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $$L^p(w)$$ L p ( w ) -operator norms in terms of the $$A_p$$ A p -characteristic of the weight w. In order to do this we show that the operators under consideration are dominated by a suitable family of sparse operators in the space of homogeneous type $$((0,\infty ),|\cdot |,x^{2\lambda }dx)$$ ( ( 0 , ∞ ) , | · | , x 2 λ d x ) .

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantitative weighted estimates for Harmonic analysis operators in the Bessel setting by using sparse domination

2022

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“…The square function g λ ψ is a Bessel version of the Stein square function introduced in [63]. Quantitative weighted L p -inequalities for the classical Stein square function were obtained in [15]. In [16] Chen, Duong and Yan established L p -boundedness properties for Stein square function associated with operators in spaces of homogeneous type.…”

Section: Introductionmentioning

confidence: 99%

Quantitative weighted estimates for harmonic analysis operators in the Bessel setting by using sparse domination

Almeida¹,

Fariña²,

Rodríguez-Mesa³

2021

Preprint

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In this paper we obtain quantitative weighted L p -inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain L p (w)-operator norms in terms of the Ap-characteristic of the weight w. In order to do this we show that the operators under consideration are dominated by a suitable family of sparse operators in the space of homogeneous type ((0, ∞), | • |, x 2λ dx).x d dx on (0, ∞). h λ , # λ and λ τ x , x ∈ (0, ∞), are connected with ∆ λ . For every f, g ∈ S(0, ∞), the Schwartz space on (0, ∞), we have that

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“…In [27], some weighted L 2 -estimates for G α were obtained. Carro and Domingo-Salazar [9] proved weighted L p -inequalities for G α showing that, when α > n+1 2 , it can be controlled by a finite sum of sparse operators.…”

Section: Introductionmentioning

confidence: 99%

$L^p$--boundedness of Stein's square functions associated to Fourier--Bessel expansions

Almeida¹,

Dalmasso²,

Rodríguez-Mesa³

2019

Preprint

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In this paper we prove L p estimates for Stein's square functions associated to Fourier-Bessel expansions. Furthermore we prove transference results for square functions from Fourier-Bessel series to Hankel transforms. Actually, these are transference results for vector-valued multipliers from discrete to continuous in the Bessel setting. As a consequence, we deduce the sharpness of the range of p for the L p -boundedness of Fourier-Bessel Stein's square functions from the corresponding property for Hankel-Stein square functions. Finally, we deduce L p estimates for Fourier-Bessel multipliers from that ones we have got for our Stein square functions.

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Stein’s Square Function $$G_\alpha $$ G α and Sparse Operators

Cited by 6 publications

References 19 publications

Quantitative weighted estimates for Harmonic analysis operators in the Bessel setting by using sparse domination

Quantitative weighted estimates for Harmonic analysis operators in the Bessel setting by using sparse domination

Quantitative weighted estimates for harmonic analysis operators in the Bessel setting by using sparse domination

$L^p$--boundedness of Stein's square functions associated to Fourier--Bessel expansions

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