Uniform convergence with rates of general singular operators

George A. Anastassiou; Razvan A. Mezei

doi:10.4067/s0719-06462013000200001

Authors

George A. Anastassiou The University of Memphis Department of Mathematical Sciences, Memphis, TN 38152, U.S.A.
Razvan A. Mezei The University of Memphis Department of Mathematical Sciences, Memphis, TN 38152, U.S.A.

DOI:

https://doi.org/10.4067/s0719-06462013000200001

Keywords:

Best constant, general singular integral, trigonometric singular integral, modulus of smoothness, sharp inequality

Abstract

In this article we study the approximation properties of general singular integral operators over the real line. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. We apply this theory to the trigonometric singular operators.