Uniform convergence with rates of general singular operators

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DOI:

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

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.

Keywords

Best constant , general singular integral , trigonometric singular integral , modulus of smoothness , sharp inequality
  • 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.
  • Pages: 01–19
  • Date Published: 2013-06-01
  • Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

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Published

2013-06-01

How to Cite

[1]
G. A. Anastassiou and R. A. Mezei, “Uniform convergence with rates of general singular operators”, CUBO, vol. 15, no. 2, pp. 01–19, Jun. 2013.

Issue

Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal

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Articles