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Research Article | Open Access

Hardy type inequalities for the fractional relativistic operator

Luz Roncal1,2,3( )
BCAM - Basque Center for Applied Mathematics 48009 Bilbao, Spain
Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
Universidad del País Vasco/Euskal Herriko Unibertsitatea, 48080 Bilbao, Spain
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Abstract

We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer.

Keywords

trace Hardy inequalityHardy inequalityextension problemground state representationfractional operator

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Mathematics in Engineering
Volume 4 Issue 3,
June 2022
Pages 1-16
DOI: 10.3934/mine.2022018

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Cite this article:
Roncal L. Hardy type inequalities for the fractional relativistic operator. Mathematics in Engineering, 2022, 4(3): 1-16. https://doi.org/10.3934/mine.2022018

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Received: 17 February 2020
Accepted: 21 April 2020
Published: 15 June 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)