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Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group

Roncal, Luz and Thangavelu, Sundaram (2016) Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. In: ADVANCES IN MATHEMATICS, 302 . pp. 106-158.

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Official URL: http://dx.doi.org/10.1016/j.aim.2016.07.010

Abstract

We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group H-n. We prove two versions of such inequalities depending on whether the weights involved are non-homogeneous or homogeneous. In the first case, the constant arising in the Hardy inequality turns out to be optimal. In order to get our results, we will use ground state representations. The key ingredients to obtain the latter are some explicit integral representations for the fractional powers of the sublaplacian and a generalized result by M. Cowling and U. Haagerup. The approach to prove the integral representations is via the language of semigroups. As a consequence of the Hardy inequalities we also obtain versions of Heisenberg uncertainty inequality for the fractional sublaplacian. (C) 2016 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 03 Dec 2016 06:07
Last Modified: 03 Dec 2016 06:07
URI: http://eprints.iisc.ac.in/id/eprint/55215

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