On a symbol class of elliptic pseudodifferential operators

Abstract

We consider a class of symbols with prescribed smoothness and growth conditions and give examples of such symbols. The introduced class contains certain polynomial symbols and symbols with more, than polynomial growth in phase space. The corresponding pseudodifferential operators defined as the Weyl transforms of the symbols are elliptic. As an application, we give a result on isomorphisms between modulation spaces. In particular, we show that the Bessel potentials establish such isomorphisms.