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Autumn 2018 $L^p$-Hardy-Rellich and uncertainty principle inequalities on the sphere
Abimbola Abolarinwa, Timothy Apata
Adv. Oper. Theory 3(4): 745-762 (Autumn 2018). DOI: 10.15352/aot.1712-1282

Abstract

In this paper, we study the Hardy-Rellich type inequalities and uncertainty principle on the geodesic sphere. Firstly, we derive $L^p$-Hardy inequalities via divergence theorem, which are in turn used to establish the $L^p$-Rellich inequalities. We also establish Heisenberg uncertainty principle on the sphere via the Hardy-Rellich type inequalities. The best constants appearing in the inequalities are shown to be sharp.

Citation

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Abimbola Abolarinwa. Timothy Apata. "$L^p$-Hardy-Rellich and uncertainty principle inequalities on the sphere." Adv. Oper. Theory 3 (4) 745 - 762, Autumn 2018. https://doi.org/10.15352/aot.1712-1282

Information

Received: 1 January 2018; Accepted: 15 April 2018; Published: Autumn 2018
First available in Project Euclid: 10 May 2018

zbMATH: 06946375
MathSciNet: MR3856170
Digital Object Identifier: 10.15352/aot.1712-1282

Subjects:
Primary: 26D10
Secondary: 46E30, 53C21

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 4 • Autumn 2018
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