Lp Convergence with Rates of Smooth Poisson-Cauchy Type Singular Operators

Abstract

In this article we continue the study of smooth Poisson-Cauchy Type singular integral operators on the line regarding their convergence to the unit operator with rates in the Lp norm, p greater equal one. The related established inequalities involve the higher order Lp modulus of smoothness of the engaged function or its higher order derivative.