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Comptes Rendus Mathématique
Volume 337, n° 1
pages 13-18 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00257-7
Received : 1 October 2002 ;  accepted : 16 May 2003
Complex interpolation between two weighted Bergman spaces on tubes over symmetric cones

David  Békollé,  Jocelyn  Gonessa,  Cyrille  Nana
Université de Yaoundé I, faculté des sciences, département de mathématiques, BP 812, Yaoundé, Cameroon 

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We prove that the complex interpolation space  ,  , between two weighted Bergman spaces   and   on the tube in  ,   over an irreducible symmetric cone of   is the weighted Bergman space   with  . Here,   and   where   denotes the rank of the cone. We then construct an analytic family of operators and an atomic decomposition of functions, which are related to this interpolation result. To cite this article: D. Békollé et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

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Nous donnons une démonstration du fait que par la méthode complexe, l'espace d'interpolation  ,  , entre deux espaces de Bergman à poids   et   est l'espace de Bergman à poids   avec  , dans le tube de  ,  , au-dessus d'un cône symétrique irréductible de   Ici,  ,  , où   désigne le rang du cône. Nous construisons ensuite une famille analytique d'opérateurs et une décomposition atomique de fonctions, qui sont en relation avec ce résultat d'interpolation. Pour citer cet article : D. Békollé et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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