Comptes Rendus
no. 21-22
Harmonic Analysis/Calculus of Variations
Fractional integrals and Ap-weights: A sharp estimate
[Intégrales fractionnaires et Ap-poids : une estimation optimale]

Présenté par : Haïm Brezis

Teresa Alberico1 ; Andrea Cianchi2 ; Carlo Sbordone1
1 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy
2 Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy
Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1265-1270.

On considère une inégalité à poids Ap, pour des potentiels de Riesz dans Rn. La constante de l'inégalité dépend de la constante Ap du poids. On donne la forme exacte de la dépendance, en particulier on précise l'exposant optimal de la constante Ap du poids.

We are concerned with an inequality, with an Ap weight, for Riesz potentials in Rn. The constant in the relevant inequality is known to depend on the Ap constant of the weight. We find the exact form of this dependence. In particular, we exhibit the optimal exponent for the Ap constant of the weight.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.09.001

Teresa Alberico 1 ; Andrea Cianchi 2 ; Carlo Sbordone 1

1 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy
2 Dipartimento di Matematica e Applicazioni per l'Architettura, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy 
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     title = {Fractional integrals and $ {A}_{p}$-weights: {A} sharp estimate},
     journal = {Comptes Rendus. Math\'ematique},
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Teresa Alberico; Andrea Cianchi; Carlo Sbordone. Fractional integrals and $ {A}_{p}$-weights: A sharp estimate. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1265-1270. doi : 10.1016/j.crma.2009.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.001/

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