Sobolev spaces and the Cayley transform

Astengo, Francesca; Di Blasio, Bianca

doi:10.1090/S0002-9939-05-08278-X

Sobolev spaces and the Cayley transform
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by Francesca Astengo and Bianca Di Blasio

Proc. Amer. Math. Soc. 134 (2006), 1319-1329

DOI: https://doi.org/10.1090/S0002-9939-05-08278-X

Published electronically: October 4, 2005

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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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