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On bilinear Hardy inequality and corresponding geometric mean inequality

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Abstract

The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case \(1< q, p_1, p_2<\infty \) with \(q \ge \max (p_1,p_2)\).

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Acknowledgements

The work of first author, has been partially supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) [Grant No. FR17-589], by Grant 18-00580S of the Czech Science Foundation and RVO:67985840. The second author acknowledges the MATRICS Research Grant No. MTR/2017/000126 of SERB, Department of Science and Technology, India.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czech Republic

    Amiran Gogatishvili

  2. Department of Mathematics, South Asian University, Chanakya Puri, New Delhi, 110021, India

    Pankaj Jain & Saikat Kanjilal

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  1. Amiran Gogatishvili
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  2. Pankaj Jain
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  3. Saikat Kanjilal
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Correspondence to Amiran Gogatishvili.

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Gogatishvili, A., Jain, P. & Kanjilal, S. On bilinear Hardy inequality and corresponding geometric mean inequality. Ricerche mat 71, 581–608 (2022). https://doi.org/10.1007/s11587-020-00536-2

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  • DOI: https://doi.org/10.1007/s11587-020-00536-2

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