2015/08/04 by Luz Roncal, Sundaram Thangavelu, Roncal, L. +1 · 3 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.1508.00714
openalex publication_date 2015/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.