Pseudolocality and Microlocality of General Classes of Pseudodifferential Operators

Abstract

We study the pseudolocality and microlocality of pseudodifferential operators with general symbols. We treat the problem of pseudo– and microlocality, along finite dimensional linear subspaces, of the Weyl quantization and also generalize some results of Parenti and Rodino to the case of the Weyl–Hormander calculus of pseudodifferential operators. We do not require that the metric, in the definition of the symbol, is decomposable, σ temperate or satisfy the uncertainty principle neither the weight function of the symbol has to be σ — g temperate. Instead, we assume weaker conditions on the metric and the weight function and the only extra condition we are assuming on the symbol is one of its essential support.