Regularity properties of singular integral operators

Abstract

For s>0, we consider bounded linear operators from $D(ℝ^n)$ into $D'(ℝ^n)$ whose kernels K satisfy the conditions $|∂^{γ}_{x}K(x,y)| ≤ C_{γ}|x-y|^{-n+s-|γ|}$ for x≠y, |γ|≤ [s]+1, $|∇_{y} ∂^{γ}_{x} K(x,y)| ≤ C_{γ}|x-y|^{-n+s-|γ|-1}$ for |γ|=[s], x≠y. We es