An integral representation of pseudo-differential operators involving weinstein transform

Abstract

In the present paper, we study the continuity property of pseudo-differential operators associated with the Weinstein transform on Schwartz space S∗(Rn+1) and find the integral representation of pseudo-differential operators Tσ associated to a symbol σ∈ Sm. Using aforesaid theory, we establish the Lα,sp- boundedness of pseudo-differential operators associated with the Weinstein transform. An application of pseudo-differential operators involving Weinstein transform in heat equation is discussed. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.