Symmetrically global pseudo-differential operators involving the Weinstein transform

Abstract

In this paper, boundedness and compactness results for symmetrically global pseudo-differential operator on Lαp(R+n+1) -type Sobolev space Hαr,s,p of order (r, s) are investigated by exploiting the theory of the Weinstein transform. Using symmetrically global symbol σ(x, ξ) in Sm1,m2,m1,m2∈R , we have discussed various properties of minimal–maximal pseudo-differential operators involving the Weinstein transform. The weak solution of the symmetrically global pseudo-differential equation is obtained by using aforesaid theory. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.