Estimations limites pour la solution canonique de l'équation ...u = f.
Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in...
Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds of pseudoconvex domains to all of even in quite simple situations; The spaces are, in general, not at all preserved. Also the image of the Hilbert space under the restriction to can have a very strange structure.
Nous montrons qu’une fonction holomorphe sur un sous-ensemble analytique transverse d’un domaine borné strictement pseudoconvexe de admet une extension dans si et seulement si elle vérifie une condition de type à poids sur ; la démonstration est en partie basée sur la résolution de l’équation avec estimations de type “mesures de Carleson”.