Pseudo-differential operators with non regular symbols. (English) Zbl 0695.47047

Marschall, Jürgen

Berlin: Freie Univ. Berlin, FB Math., Thesis. 139 p. (1985).

This work is concerned with pseudo-differential operators with nonsmooth symbols which belong to Hölder-Zygmund spaces. The author develops a calculus with pseudo-differential operators with such a symbol and extends several known properties of pseudo-differential operators with regular symbols such as the continuity and compacity from \(H^{s,p}\) to \(H^{s-m,p}\). Some applications to the construction of a parametrix for elliptic differential operators are given.

Reviewer: V.Barbu

MSC:

47Gxx	Integral, integro-differential, and pseudodifferential operators
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35S05	Pseudodifferential operators as generalizations of partial differential operators

Keywords:

pseudo-differential operators with nonsmooth symbols which belong to Hölder-Zygmund spaces; construction of a parametrix for elliptic differential operators