Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group
- Roncal, L. 1
- Thangavelu, S. 2
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1
Universidad de La Rioja
info
- 2 Department of Mathematics, Indian Institute of Science, Bangalore, India
ISSN: 0001-8708
Argitalpen urtea: 2016
Alea: 302
Orrialdeak: 106-158
Mota: Artikulua
Beste argitalpen batzuk: Advances in Mathematics
Laburpena
We prove Hardy inequalities for the conformally invariant fractional powers of the sublaplacian on the Heisenberg group Hn. 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. © 2016 Elsevier Inc.