La conjecture de la couronne en analyse complexe et p-adique
Nous répondons à une conjecture de R. Coifman et R. Rochberg : dans le complexifié du cône sphérique de , le dual de la classe de Bergman s’obtient comme projection de Bergman de et coïncide avec la classe de Bloch des fonctions holomorphes. Nous examinons également le cas d’un produit de domaines.
In this note by using techniques similar to that of [2] and [3], we study the local polynomial convexity of perturbation of union of two totally real planes meeting along a real line.
We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
Linear topological properties of the Lumer-Smirnov class of the unit polydisc are studied. The topological dual and the Fréchet envelope are described. It is proved that has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for .
Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.