Uniform Convergence With Rates of General Singular Operators
Anastassiou, George A.
Mezei, Razvan A.
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.