A calculus of abstract edge pseudodifferential operators of type $\varrho,\delta$

Abstract

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 H\"ormander's $\varrho,\delta$ calculus, where $0 \leq \delta < \varrho \leq 1$. 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 $1,\delta$ for $0 < \delta < 1$ appear naturally. Some of the results of this paper 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.