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

Abstract

After proving a result of continuity for pseudo-differential operators whose symbols belong to Hölder spaces and satisfy a decay of quasihomogeneous type, the authors construct a suitable symbolic calculus and a parametrix for quasi-elliptic operators; these tools are applied to the study of quasi-elliptic linear partial differential equations with Hölder coefficients.