On the Improved Form of the Bounded Theorem for Pseudo-Differential Operators

Caldern A.P.et al.were studied a class of the bounded pseudo-differential operators of order -M and type ρ,δ_1,δ_2, and showed them to be bounded in L~2 provided that 0≤ρ≤δ_1<1, 0≤ρ≤δ_2<1 and M/n≥1/2(δ_1+δ_2)-ρ.Hrmander et al.have shown that if the aforecited conditions are not valid, then the conclusion that A is bounded in L~2 isn't necessarily right. Caldern et al. settled the borderline case and remove the restriction on the support of α.