Mellin Operators with Asymptotics on Manifolds with Corners

We study Mellin operators on a singular manifold M with corners of second order, locally modelled on a cone B-Delta = ((R) over bar(+) Chi B)/({0} Chi B), where B is a compact C-infinity manifold with smooth edge. Such operators, together with the so-called Green operators, constitute the asymptotic part of the pseudo-differential calculus on M. They reflect specific asymptotic properties of solutions to corner-degenerate elliptic equations near edge and corner singularities. In the present case they act on spaces with double weights and iterated asymptotics. Due to the role of M as a step in the hierarchy of manifolds with higher singularities, we focus on the so-called continuous asymptotics, which are based on vector-valued analytic functionals in the complex plane of the Mellin covariable.