$L_{p}$ Convergence with rates of smooth Gauss-Weierstrass singular operators

Abstract

In this article we study the smooth Gauss-Weierstrass singular integral operators on the line regarding their convergence to the unit operator with rates in the $L_{p}$ norm, $p\geq 1$. The related established inequalities involve the higher order $L_{p}$ modulus of smoothness of the engaged function or its higher order derivative.