Pseudodifferential operators on manifolds with edges

We define pseudodifferential operators on manifolds with singularities of smooth edge type and construct a calculus of such operators. We prove that a pseudodifferential operator is invariant with respect to a certain natural class of diffeomorphisms of the manifold. We introduce a scale of function spaces (weighted analogs of the Sobolev classes) and establish theorems on boundedness of pseudodifferential operators in this scale. Bibliography: 8 titles. Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 162–214.