### $L^p$-Hardy-Rellich and uncertainty principle inequalities on the sphere

#### 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.

#### Article information

Source

Dates
Accepted: 15 April 2018
First available in Project Euclid: 10 May 2018

https://projecteuclid.org/euclid.aot/1525917618

Digital Object Identifier
doi:10.15352/aot.1712-1282

#### Citation

Abolarinwa, Abimbola; Apata, Timothy. $L^p$-Hardy-Rellich and uncertainty principle inequalities on the sphere. Adv. Oper. Theory, advance publication, 10 May 2018. doi:10.15352/aot.1712-1282. https://projecteuclid.org/euclid.aot/1525917618

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