Properties of M−hyoellipticity for pseudo differential operators

In this paper we study properties of symbols such that these belong to class of symbols sitting inside S_{\rho,\varphi}^m that we shall introduce as the following. So for because hypoelliptic pseudodifferential operators play a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudo differential operators for which define base on this class of symbols. Also we consider maximal and minimal operators of M-hypoelliptic pseudo differential operators and we express some results about these operators.

Keywords:

pseudo differential operator , elliptic operator , hypoelliptic operator , parametrix operator