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arXiv · 2101.08460

An extension problem and Hardy's inequality for the fractional Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type

Mithun Bhowmik·Sanjoy Pusti
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Abstract

In this paper we study an extension problem for the Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type and use the solution to prove Hardy-type inequalities for fractional powers of the Laplace-Beltrami operator. Next, we study the mapping properties of the extension operator. In the last part we prove Poincar\'e-Sobolev inequalities on these spaces.

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Mithun Bhowmik, Sanjoy Pusti. 2021-01-21. An extension problem and Hardy's inequality for the fractional Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type. https://arxiv.org/abs/2101.08460

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