Centered Hardy–Littlewood maximal operator on the real line: Lower bounds

Ivanisvili, Paata; Zbarsky, Samuel

doi:10.1016/j.crma.2019.03.003

Mathematical analysis/Harmonic analysis

Centered Hardy–Littlewood maximal operator on the real line: Lower bounds
[Fonction maximale centrée de Hardy–Littlewood : bornes inférieures]

Présenté par : the Editorial Board

Ivanisvili, Paata ¹ ; Zbarsky, Samuel ¹

¹ Princeton University, Princeton, NJ, USA

Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 339-344.

Résumé
Abstract

Soient $1 < p < \infty$ et M la fonction maximale de Hardy–Littlewood sur $R$ . Nous étudions l'existence d'un $ε = ε (p) > 0$ tel que $| | M f | |_{p} \geq (1 + ε) | | f | |_{p}$ . Nous l'établissons pour $1 < p < 2$ . Pour $2 \leq p < \infty$ , nous prouvons l'inégalité pour les fonctions indicatrices et les fonctions unimodales.

For $1 < p < \infty$ and M the centered Hardy–Littlewood maximal operator on $R$ , we consider whether there is some $ε = ε (p) > 0$ such that $| | M f | |_{p} \geq (1 + ε) | | f | |_{p}$ . We prove this for $1 < p < 2$ . For $2 \leq p < \infty$ , we prove the inequality for indicator functions and for unimodal functions.

Reçu le : 2018-10-09
Accepté le : 2019-03-11
Publié le : 2019-03-26

DOI : 10.1016/j.crma.2019.03.003

Affiliations des auteurs :

Ivanisvili, Paata ¹ ; Zbarsky, Samuel ¹

¹ Princeton University, Princeton, NJ, USA

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     author = {Ivanisvili, Paata and Zbarsky, Samuel},
     title = {Centered {Hardy{\textendash}Littlewood} maximal operator on the real line: {Lower} bounds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {339--344},
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Ivanisvili, Paata; Zbarsky, Samuel. Centered Hardy–Littlewood maximal operator on the real line: Lower bounds. Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 339-344. doi : 10.1016/j.crma.2019.03.003. http://www.numdam.org/articles/10.1016/j.crma.2019.03.003/

Bibliographie
Cité par

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