Abstract
Let σ be the geodesic inversion on a Heisenberg type group N with homogeneous dimension Q, and denote by S the jacobian of σ. We prove that, for $ - \frac{1}{2}Q< \alpha< \frac{1}{2}Q$ , the operators $T_\alpha :f \mapsto S^{1/2 - \alpha /Q} (f \circ \sigma )$ are bounded on certain homogeneous Sobolev spaces $\mathcal{H}^\alpha (N)$ if and only if N is an Iwasawa N-group.
Funding Statement
The research for this paper was carried out at the University of New South Wales. The authors thank the Italian G.N.A.M.P.A., the Progetto Cofinanziato M.U.R.S.T. “Analisi Armonica”, and the School of Mathematics of the University of New South Wales for their support.
Citation
Francesca Astengo. Bianca Blasio. "Geodesic inversion and Sobolev spaces on Heisenberg type groups." Ark. Mat. 43 (1) 51 - 67, April 2005. https://doi.org/10.1007/BF02383610
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