A calculus of abstract edge pseudodifferential operators of type \varrho,δ

2014/03/24 by Thomas Krainer, Krainer, Thomas
Mathematics · #35S05 (Primary) 47G30 #58J32 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35S05 #msc:47G30 #msc:58J32

paper · pdf · doi:10.48550/arxiv.1403.6100

26 pages

arxiv created 2014/03/24 · arxiv updated 2014/03/25

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 Hörmander's \varrho,δ calculus, where 0 ≤ δ< \varrho ≤ 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 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.

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