Properties of $M$−hyoellipticity for pseudo differential operators

Document Type : Research Paper


Department of Mathematics, University of Mazandaran, Babolsar 47416-1468, Iran.


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.