Geodesic inversion and Sobolev spaces on Heisenberg type groups

Francesca Astengo Dipartimento di Matematica, Università di Genova Bianca Di Blasio Dipartimento di Matematica, Università di Roma “Tor Vergata”

TBD mathscidoc:1701.333045

Arkiv for Matematik, 43, (1), 51-67, 2003.5
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.
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@inproceedings{francesca2003geodesic,
  title={Geodesic inversion and Sobolev spaces on Heisenberg type groups},
  author={Francesca Astengo, and Bianca Di Blasio},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203612684775854},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={1},
  pages={51-67},
  year={2003},
}
Francesca Astengo, and Bianca Di Blasio. Geodesic inversion and Sobolev spaces on Heisenberg type groups. 2003. Vol. 43. In Arkiv for Matematik. pp.51-67. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203612684775854.
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