On two conjectures of Hartshorne's.
We generalize classical results for plurisubharmonic functions and hyperconvex domain to q-plurisubharmonic functions and q-hyperconvex domains. We show, among other things, that Bq-regular domains are q-hyperconvex. Moreover, some smoothing results for q-plurisubharmonic functions are also given.
On résout le pour les formes admettant une valeur au bord au sens des courants sur un domaine strictement pseudoconvexe de .