Weighted Hardy inequalities with sharp constants
J. Korean Math. Soc.
Published online December 4, 2019
Aigerim Kalybay and Ryskul Oinarov
KIMEP University, L.N. Gumilyov Eurasian National University
Abstract : 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 : 26D10, 26D15, 39A21
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