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April 2005 Geodesic inversion and Sobolev spaces on Heisenberg type groups
Francesca Astengo, Bianca Blasio
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Ark. Mat. 43(1): 51-67 (April 2005). DOI: 10.1007/BF02383610

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

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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

Information

Received: 6 May 2003; Published: April 2005
First available in Project Euclid: 31 January 2017

zbMATH: 1092.43010
MathSciNet: MR2134698
Digital Object Identifier: 10.1007/BF02383610

Rights: 2005 © Institut Mittag-Leffler

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