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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sobolev spaces and the Cayley transform


Authors: Francesca Astengo and Bianca Di Blasio
Journal: Proc. Amer. Math. Soc. 134 (2006), 1319-1329
MSC (2000): Primary 43A80; Secondary 43A85, 43A15
Published electronically: October 4, 2005
MathSciNet review: 2199175
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Abstract | References | Similar Articles | Additional Information

Abstract: The generalised Cayley transform  $ \mathcal{C}$ from an Iwasawa $ N$-group into the corresponding real unit sphere  $ \mathbb{S}$ induces isomorphisms between suitable Sobolev spaces $ \mathcal{H}^\alpha(\mathbb{S})$ and $ \mathcal{H}^\alpha(N)$. We study the differential of  $ \mathcal{C}$, and we obtain a criterion for a function to be in  $ \mathcal{H}^\alpha(\mathbb{S})$.


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Additional Information

Francesca Astengo
Affiliation: Dipartimento di Matematica, Università di Genova, 16146 Genova, Italia
Email: astengo@dima.unige.it

Bianca Di Blasio
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, 00133 Roma, Italia
Email: diblasio@mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08278-X
PII: S 0002-9939(05)08278-X
Keywords: Heisenberg type groups, Sobolev spaces
Received by editor(s): November 18, 2004
Published electronically: October 4, 2005
Additional Notes: The authors thank the School of Mathematics of the University of the New South Wales and the Italian G.N.A.M.P.A. for their support
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society