Abstract
The infinite pseudo-differential operator on WM(Rn) space is introduced and its various properties are studied. A general class of symbols θ(x,ξ) is introduced and then it is proved that the pseudo-differential operator Aθφ 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 σ(x,ξ) for ξ = 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 < ∞. The Sobolev space of type Gs,p(Rn) is introduced and its properties are studied.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
