The generalised Cayley transform C from an Iwasawa N-group into the corresponding real unit sphere S induces isomorphisms between suitable Sobolev spaces H_(S) and H_(N). We study the differential of C, and we obtain a criterion for a function to be in H_(S).
Astengo, F., DI BLASIO, B. (2006). Sobolev spaces and the Cayley transform. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134, 1319-1329 [10.1090/S0002-9939-05-08278-X].
Sobolev spaces and the Cayley transform
DI BLASIO, BIANCA
2006
Abstract
The generalised Cayley transform C from an Iwasawa N-group into the corresponding real unit sphere S induces isomorphisms between suitable Sobolev spaces H_(S) and H_(N). We study the differential of C, and we obtain a criterion for a function to be in H_(S).
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