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Multidimensional Frank–Laptev–Weidl improvement of the hardy inequality

Part of: Linear function spaces and their duals Inequalities Partial differential equations

Published online by Cambridge University Press:  11 January 2024

Prasun Roychowdhury ,
Michael Ruzhansky Open the ORCID record for Michael Ruzhansky [Opens in a new window]  and
Durvudkhan Suragan Open the ORCID record for Durvudkhan Suragan [Opens in a new window]
Prasun Roychowdhury
Affiliation:
Mathematics Division, National Center for Theoretical Sciences, NTU, Taipei City, Taiwan (prasunroychowdhury1994@gmail.com)
Michael Ruzhansky
Affiliation:
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium School of Mathematical Sciences, Queen Mary University of London, London, UK (michael.ruzhansky@ugent.be)
Durvudkhan Suragan
Affiliation:
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan (durvudkhan.suragan@nu.edu.kz)
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Abstract

We establish a new improvement of the classical Lp-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one-dimensional Hardy inequality. Using some radialisation techniques of functions and then exploiting symmetric decreasing rearrangement arguments on the real line, the new multidimensional version of the Hardy inequality is given. Some consequences are also discussed.

Keywords

Hardy inequalitysharp constantsymmetric rearrangementsuncertainty principle

MSC classification

Primary: 26D10: Inequalities involving derivatives and differential and integral operators 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 1 , February 2024 , pp. 151 - 167
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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