Compactness for the weighted Hardy operator in variable exponent spaces

Farman Mamedov; Sayali Mammadli

doi:10.1016/j.crma.2016.12.010

Harmonic analysis

Compactness for the weighted Hardy operator in variable exponent spaces

Presented by: the Editorial Board

Farman Mamedov ^1,²; Sayali Mammadli 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, Volume 355 (2017) no. 3, pp. 325-335.

Abstract
Résumé

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)

to

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

.

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)

.

Received: 2016-07-14
Accepted: 2017-01-10
Published online: 2017-02-10

DOI: 10.1016/j.crma.2016.12.010

Author's affiliations:

Farman Mamedov ^{1, 2}; Sayali Mammadli 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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     pages = {325--335},
     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2016.12.010},
     language = {en},
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Farman Mamedov; Sayali Mammadli. Compactness for the weighted Hardy operator in variable exponent spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 3, pp. 325-335. doi : 10.1016/j.crma.2016.12.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.12.010/

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