Regularity for quasi-elliptic pseudo-differential operators with symbols in Holder classes

In the present talk a results of continuuty in Sobolev spaces for pseudodifferential operators with symbols in Holder classes are proved. All the matter is considered in the quasi-homogeneous framework, in the sense of Lascar symbol, and we let symbols satisfy a decay at the infinity of type 1,1. Suitable symbolic calculus and parametrix are considered for quasi elliptic pseudodifferential operators. All the tools are applied to the study of quasi-elliptic linear partial differential equations with Holder coefficients.