Symmetrically global pseudo-differential operators involving the Weinstein transform

In this paper, boundedness and compactness results for symmetrically global pseudodifferential operator on L p a(Rn+1 +)-type Sobolev space Hr,s,p a of order (r, s) are investigated by exploiting the theory of the Weinstein transform. Using symmetrically global symbol s(x,.) in S-m1,(m2,) m1, m2. epsilon R, we have discussed various properties of minimal-maximal pseudo-differential operators involving theWeinstein transform. The weak solution of the symmetrically global pseudo-differential equation is obtained by using aforesaid theory.