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

摘要

In this paper we study an extension problem for the Laplace-Beltrami operator on Riemannian symmetric spaces of non-compact 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 Poincare-Sobolev inequalities on these spaces. (C) 2022 Elsevier Inc. All rights reserved.