Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.

This work is the continuation of two earlier ones by the author and stimulated by many more recent contributions. We develop a very general calculus of pseudodifferential operators with microlocally defined normed symbol spaces. The goal was to attain the natural degree of generality in the case when the underlying metric on the cotangent space is constant. We also give sufficient conditions for our operators to belong to Schatten–von Neumann classes.