Pseudo-differential operators in H\"older spaces revisited. Weyl-H\"ormander calculus and Ruzhansky-Turunen classes

In this work we obtain continuity results on H"older spaces for operators belonging to a Weyl-H"ormander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With our results we recover some historical H"older boundedness theorems (see R. Beals \cite{Be,Be2}). The action of (periodic) Ruzhansky-Turunen classes of pseudo-differential operators on H"older spaces also will be investigated.