Advances in Operator Theory

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

Abimbola Abolarinwa and Timothy Apata

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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

Adv. Oper. Theory, Advance publication (2018), 18 pages.

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

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Digital Object Identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Hardy inequalities Rellich inequalities uncertainty principle geodesic sphere compact manifold


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.

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