q-Plurisubharmonicity and q-pseudoconvexity in cn

Resum

We generalize classical results for plurisubharmonic functions and hyperconvex domain to $q$-plurisubharmonic functions and $q$-hyperconvex domains. We show, among other things, that $B_q$-regular domains are $q$-hyperconvex. Moreover, some smoothing results for $q$-plurisubharmonic functions are also given.