Fractional integrals and $ {A}_{p}$-weights: A sharp estimate

Teresa Alberico; Andrea Cianchi; Carlo Sbordone

doi:10.1016/j.crma.2009.09.001

Harmonic Analysis/Calculus of Variations

Fractional integrals and

A_{p}

-weights: A sharp estimate
[Intégrales fractionnaires et

A_{p}

-poids : une estimation optimale]

Présenté par : Haïm Brezis

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

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1265-1270.

Résumé
Abstract

On considère une inégalité à poids $A_{p}$ , pour des potentiels de Riesz dans $R^{n}$ . La constante de l'inégalité dépend de la constante $A_{p}$ du poids. On donne la forme exacte de la dépendance, en particulier on précise l'exposant optimal de la constante $A_{p}$ du poids.

We are concerned with an inequality, with an $A_{p}$ weight, for Riesz potentials in $R^{n}$ . The constant in the relevant inequality is known to depend on the $A_{p}$ constant of the weight. We find the exact form of this dependence. In particular, we exhibit the optimal exponent for the $A_{p}$ constant of the weight.

Accepté le : 2009-07-12
Publié le : 2009-10-28

DOI : 10.1016/j.crma.2009.09.001

Affiliations des auteurs :

Teresa Alberico ¹ ; Andrea Cianchi ² ; Carlo Sbordone ¹

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     author = {Teresa Alberico and Andrea Cianchi and Carlo Sbordone},
     title = {Fractional integrals and $ {A}_{p}$-weights: {A} sharp estimate},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1265--1270},
     publisher = {Elsevier},
     volume = {347},
     number = {21-22},
     year = {2009},
     doi = {10.1016/j.crma.2009.09.001},
     language = {en},
}

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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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