Pseudo-differential operators in Hölder spaces revisited. Weyl-Hörmander calculus and Ruzhansky-Turunen classes
arXiv:1806.09245
Abstract
In this work we obtain continuity results on Hölder spaces for operators belonging to a Weyl-Hörmander calculus for metrics such that the class of the associated operators contains, in particular, certain hypoelliptic laplacians. With our results we recover some historical Hölder boundedness theorems (see R. Beals \cite{Be,Be2}). The action of (periodic) Ruzhansky-Turunen classes of pseudo-differential operators on Hölder spaces also will be investigated.
16 pages