Sharp Multiplier Theorem for Multidimensional Bessel Operators

Kania, Edyta; Preisner, Marcin

doi:10.1007/s00041-019-09667-z

Cited by 6 publications

(3 citation statements)

References 35 publications

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“…From here, by the arguments from the above mentioned proof, see (15), we arrive at the lower bound for δ in (A).…”

Section: Fractional Integralsmentioning

confidence: 70%

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Langowski¹,

Nowak²

2020

Preprint

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We prove sharp power-weighted L p , weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator Bν in the exotic range of the parameter −∞ < ν < 1. Moreover, in the same framework, we characterize basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical g-function and fractional integrals (Riesz potential operators).

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“…From here, by the arguments from the above mentioned proof, see (15), we arrive at the lower bound for δ in (A).…”

Section: Fractional Integralsmentioning

confidence: 70%

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Langowski¹,

Nowak²

2020

Preprint

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“…Recently, harmonic analysis related to the classical Bessel operator has been extensively developed, see e.g. [1][2][3][4][5][6]8,12,14,19,20] and references therein. In particular, the Hardy space…”

Section: Hardy Spaces Associated With the Classical Bessel Operatormentioning

confidence: 99%

The atomic Hardy space for a general Bessel operator

Kania-Strojec

2021

Monatsh Math

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We study Hardy spaces associated with a general multidimensional Bessel operator $$\mathbb {B}_\nu $$ B ν . This operator depends on a multiparameter of type $$\nu $$ ν that is usually restricted to a product of half-lines. Here we deal with the Bessel operator in the general context, with no restrictions on the type parameter. We define the Hardy space $$H^1$$ H 1 for $$\mathbb {B}_\nu $$ B ν in terms of the maximal operator of the semigroup of operators $$\exp (-t\mathbb {B}_\nu )$$ exp ( - t B ν ) . Then we prove that, in general, $$H^1$$ H 1 admits an atomic decomposition of local type.

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“…The study of harmonic analysis associated with Bessel operators was begun by Muckenhoupt and Stein ([58]) and continued by Andersen and Kerman ( [3]) and Stempak ([65]). In the last fifteen years many problems concerning to the harmonic analysis in the Bessel context has been studied ( [4], [5], [6], [7], [8], [21], [24], [26], [32], [41], [42], [44], [60], [66], [67] and [68]).…”

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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Sharp Multiplier Theorem for Multidimensional Bessel Operators

Abstract: Consider the multidimensional Bessel operator

Cited by 6 publications

References 35 publications

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

The atomic Hardy space for a general Bessel operator

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

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