On Semigroups Generated by Sums of Even Powers of Dunkl Operators

Dziubański, Jacek; Hejna, Agnieszka

doi:10.1007/s00020-021-02646-4

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…More information about applications to CMS models can be found in [18], and an overview of their use in probability theory is contained in [9]. For more recent work on functional inequalities for Dunkl operators see [19], [20], [3], [1], [7], [21], [15], and references therein.…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

Velicu

2022

Electron. J. Probab.

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In this paper we study several inequalities of log-Sobolev type for Dunkl operators.After proving an equivalent of the classical inequality for the usual Dunkl measure µ k , we also study a number of inequalities for probability measures of Boltzmann type of the form e −|x| p dµ k . These are obtained using the method of U -bounds. Poincaré inequalities are obtained as consequences of the log-Sobolev inequality. The connection between Poincaré and log-Sobolev inequalities is further examined, obtaining in particular tight log-Sobolev inequalities. Finally, we study application to exponential integrability and to functional inequalities for a class of singular Boltzmann-Gibbs measures.

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Section: Introductionmentioning

confidence: 99%

Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

Velicu

2022

Electron. J. Probab.

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“…After the Dunkl's paper ( [18]) appeared the theory has been developed extensively ( [16], [17], [19], [20], [50][51][52][53][54][55], [58] and [59]). Recently, harmonic analysis associated with Dunkl operators has gained a lot of interest ( [3][4][5], [21][22][23][24][25][26][27][28], [30], [32], [34][35][36], [45] and [57]).…”

Section: Introductionmentioning

confidence: 99%

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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“…The study of fundamental solutions is central in the theory of linear parabolic PDEs. For more results on heat kernel estimates for higher-order operators we refer to [6,7,9,10,11,13,15,16]. See also [14,17] for related results specific to fourth-order operators.…”

Section: Introductionmentioning

confidence: 99%

Heat kernel estimates for fourth-order non-uniformly elliptic operators with non-strongly convex symbols

Barbatis¹,

Panagiotis²

2022

ejde

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We obtain heat-kernel estimates for fourth-order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This entails certain difficulties as it is known that, as opposed to the strongly convex case, there is no absolute exponential constant. Our estimates involve sharp constants and Finsler-type distances that are inducedby the operator symbol. The main result is based on two general hypotheses, a weighted Sobolev inequality and an interpolation inequality, which are related to the singularity or degeneracy of the coefficients.

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On Semigroups Generated by Sums of Even Powers of Dunkl Operators

Cited by 4 publications

References 24 publications

Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

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

Heat kernel estimates for fourth-order non-uniformly elliptic operators with non-strongly convex symbols

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