Infinite pseudo-differential operators on Wm(Rh) space

Abstract

The infinite pseudo-differential operator on WM (Rn) space is introduced and its various properties are studied. A general class of symbols 9(x,) is introduced and then it is proved that the pseudo-differential operator Aq <p is a continuous linear mapping from WM (Rn) into itself. An Lp(Rn)-boundedness result for the pseudo-differential operator associated with a general class of symbols a(x,) for = u + it is obtained. It is shown that the pseudo-differential operator is a bounded linear operator from Lp (Rn) into Lp (Rn ) for 1 < p < 1. The Sobolev space of type Gs,p(Rn) is introduced and its properties are studied. © 2012, by Oldenbourg Wissenschaftsverlag, Edinburg, Germany. All rights reserved.