On a class of pseudodifferential operators in $\mathbb R^m$ and on stratified manifolds

A class of pseudodifferential operators in a subdomain of $\mathbb R^m$ that is well adapted to the transfer to manifolds with (intersecting) edges of various dimensions is considered. A version of symbolic calculus is discussed. The operators in question act in Sobolev spaces with weighted norms. Stratified manifolds (with edges as strata) are introduced and pseudodifferential operators on such manifolds are defined.