Sur la norme de Fourier. II.
Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.
We prove a Weierstrass division formula for Whitney jets ∂̅-flat on arbitrary compact subsets of the complex plane. We also give results for Carleman classes.
On étudie les convexes compacts , tels que pour toute partie de , l’ensemble des fonctions affines continues sur , comprises entre 0 et 1, et nulles sur , ait un plus grand élément. On caractérise ces convexes compacts comme ceux dont des quotients affines convenables sont des chapeaux universels de cônes à base compacte. On a une “complémentation naturelle” sur le treillis des faces exposés de , et des liens remarquables entre ce treillis et l’espace des fonctions affines continues sur .