A calculus of abstract edge pseudodifferential operators of type ρ, δ

In this paper, we expand on B.-W. Schulze’s abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on Hörmander’s ρ, δ calculus, where 0 ≤ δ < ρ ≤ 1. This expansion is motivated by recent work on boundary value problems for elliptic wedge operators with variable indicial roots by G. Mendoza and the author, where operators of type 1, δ for 0 < δ < 1 appear naturally. Some of the results of this chapter also represent improvements over the existing literature on the standard abstract edge calculus of operators of type 1, 0, such as trace class mapping properties of operators in abstract wedge Sobolev spaces. The presentation in this paper is largely self-contained to allow for an independent reading.