ESTIMATE OF THE BEST CONSTANT OF DISCRETE HARDY-TYPE INEQUALITY WITH MATRIX OPERATOR SATISFYING THE OINAROV CONDITION

Kalybay A. Shalginbayeva S.
2024 L.N. Gumilyov Eurasian National University

Eurasian Mathematical Journal
2024 #15 Issue 2 42 - 47 pp.

This paper studies the weighted inequality of Hardy-type in discrete form for matrix operators satisfying the Oinarov condition. Necessary and sufficient conditions on the weight sequences under which the Hardy-type inequality holds were found in [13] for the case 1 < p ≤ q < ∞, in [14] for the case 1 < q < p < ∞, and in [15] for the case 0 < p ≤ q < ∞, 0 < p ≤ 1. In this paper, we extend the result of [13] with a two-sided estimate of the inequality constant.

Hardy-type inequality , matrix operator , Oinarov condition , space of sequences , weight sequence

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KIMEP University, 4 Abay Ave, Almaty, 480100, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, Almaty, 050010, Kazakhstan
Asfendiyarov Kazakh National Medical University, 37A Zheltoksan St, Almaty, 050004, Kazakhstan

KIMEP University
Institute of Mathematics and Mathematical Modeling
Asfendiyarov Kazakh National Medical University

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