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

Abstract:

      Calderon A. P. et al. were studied a class of the bounded pseudo-differential-operators of order -M and type ρ,δ₁, δ₂, and showed them to be bounded in L² provided that 0≤ρ≤δ₁<1, 0≤ρ≤δ₂<1 and M/n≥1/2(δ₁+δ₂)-ρ. H?raander et al. have shown that if the aforecited conditions are not valid, then the conclusion that A is bounded in L² isn't necessarily right. Calderon et al. settled the borderline case and remove the restriction on the support of a.