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Eurasian Mathematical Journal, 2025, Volume 16, Number 1, Pages 86–93
DOI: https://doi.org/10.32523/2077-9879-2025-16-1-86-93 (Mi emj527) 		 
One-dimensional integral Rellich type inequalities

T. Ozawaa, P. Roychowdhuryb, D. Suraganc

a Department of Applied Physics, Waseda University, Okubo 3-4-1, Shinjuku-ku, 169-8555, Tokyo, Japan
b Dipartimento di Matematica e Applicazioni, Universita degli Studi di Milano-Bicocca, Via Cozzi 55, 20125, Milano, Italy
c Department of Mathematics, Nazarbayev University, Kabanbay batyr ave. 53, 010000, Astana, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2025-16-1-86-93
Abstract: The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy–Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy–Rellich type inequality improves the previously known result. Meanwhile, the established sharp Rellich typei ntegral inequality seems new.
Keywords and phrases: Hardy inequality, Rellich inequality, Hardy–Rellich inequality, sharp constant.
Funding agency Grant number
Committee of Science of the Ministry of Science and Higher Education of Kazakhstan AP19674900
NU program 20122022CRP1601
Japan Society for the Promotion of Science 18KK0073
19H00644
National Theoretical Science Research Center 112L104040
This research was funded by the Committee of Science of the Ministry of Science and Higher Education of Kazakhstan (Grant No. AP19674900). The paper is also partially supported by the NU program 20122022CRP1601. The first author is supported in partby JSPS Kakenhi 18KK0073, 19H00644. The second authoris partially supported by National Theoretical Science Research Center Operational Plan (Project number: 112L104040).
Received: 08.11.2024
Document Type: Article
MSC: 26D10, 35A23
Language: English
Citation: T. Ozawa, P. Roychowdhury, D. Suragan, “One-dimensional integral Rellich type inequalities”, Eurasian Math. J., 16:1 (2025), 86–93
Citation in format AMSBIB
\Bibitem{OzaRoySur25}
\by T.~Ozawa, P.~Roychowdhury, D.~Suragan
\paper One-dimensional integral Rellich type inequalities
\jour Eurasian Math. J.
\yr 2025
\vol 16
\issue 1
\pages 86--93
\mathnet{http://mi.mathnet.ru/emj527}
\crossref{https://doi.org/10.32523/2077-9879-2025-16-1-86-93}
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