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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2020; 57(3): 603-616

Online first article December 4, 2019      Printed May 1, 2020

https://doi.org/10.4134/JKMS.j190266

Copyright © The Korean Mathematical Society.

Weighted Hardy inequalities with sharp constants

Aigerim Kalybay, Ryskul Oinarov

4 Abay Avenue; 5 Munaytpasov Street

Abstract

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In the paper, we establish the validity of the weighted discrete and integral Hardy inequalities with periodic weights and find the best possible constants in these inequalities. In addition, by applying the established discrete Hardy inequality to a certain second--order difference equation, we discuss some oscillation and nonoscillation results.

Keywords: Discrete Hardy inequality, integral Hardy inequality, weight function, oscillation, difference equation

MSC numbers: Primary 26D10, 26D15, 39A21

Supported by: This work was financially supported by the Ministry of Education and Science of the Republic of Kazakhstan, Grant No. AP05130975.

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