Compactness for the weighted Hardy operator in variable exponent spaces

Mamedov, Farman; Mammadli, Sayali

doi:10.1016/j.crma.2016.12.010

Harmonic analysis

Compactness for the weighted Hardy operator in variable exponent spaces
[Compacité de l'opérateur de Hardy pondéré entre espaces d'exposant variable]

Présenté par : the Editorial Board

Mamedov, Farman ^1,² ; Mammadli, Sayali ¹

¹ Mathematics and Mechanic Institute of National Academy of Science, Baku 1141, B. Vahabzade, 9, Azerbaijan
² OilGasScientificResearchProject Inst., SOCAR, Baku 1012, H. Zardabi, 88A, Azerbaijan

Comptes Rendus. Mathématique, Tome 355 (2017) no. 3, pp. 325-335.

Résumé
Abstract

Dans cette Note, nous prouvons une condition nécessaire et suffisante pour que l'opérateur de Hardy pondéré

H_{υ, ω} f (x) = υ (x) \int_{0}^{x} f (t) ω (t) d t

agisse de façon compacte de

L^{p (\cdot)} (0, \infty)

dans

L^{q (\cdot)} (0, \infty)

In this paper, we prove a necessary and sufficiency condition for the weighted Hardy operator

H_{υ, ω} f (x) = υ (x) \int_{0}^{x} f (t) ω (t) d t

to be compactly acting from

L^{p (\cdot)} (0, \infty)

L^{q (\cdot)} (0, \infty)

Reçu le : 2016-07-14
Accepté le : 2017-01-10
Publié le : 2017-02-10

DOI : 10.1016/j.crma.2016.12.010

Affiliations des auteurs :

Mamedov, Farman ^{1, 2} ; Mammadli, Sayali ¹

¹ Mathematics and Mechanic Institute of National Academy of Science, Baku 1141, B. Vahabzade, 9, Azerbaijan
² OilGasScientificResearchProject Inst., SOCAR, Baku 1012, H. Zardabi, 88A, Azerbaijan

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     title = {Compactness for the weighted {Hardy} operator in variable exponent spaces},
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Mamedov, Farman; Mammadli, Sayali. Compactness for the weighted Hardy operator in variable exponent spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 3, pp. 325-335. doi : 10.1016/j.crma.2016.12.010. http://www.numdam.org/articles/10.1016/j.crma.2016.12.010/

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