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THE CHARACTERISATION OF THE REGULARITY OF THE JACOBIAN DETERMINANT IN THE FRAMEWORK OF POTENTIAL SPACES

Published online by Cambridge University Press:  01 February 1999

WINFRIED SICKEL  and
ABDELLAH YOUSSFI
WINFRIED SICKEL
Affiliation:
Mathematisches Institut, Fr.-Schiller-Universität, 07740 Jena, Germany
ABDELLAH YOUSSFI
Affiliation:
Equipe d'Analyse et de Math. Appliquées, Université Marne-la-Vallée, Cité Descartes, 5 BD Descartes, Champs-sur-Marne 77166, Marne-la-Vallée Cedex 2, France
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Abstract

We give necessary and sufficient conditions on the parameters s1, s2, …, sm, p1, p2, …, pm such that the Jacobian determinant extends to a bounded operator from [Hscr ]s1p1× [Hscr ]s2p2×…× [Hscr ]smpm into [Zscr ]′. Here all spaces are defined on ℝn and 2[les ]m[les ]n. In almost all cases the regularity of the Jacobian determinant is calculated exactly.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 287 - 310
Copyright
The London Mathematical Society 1999

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