CUBO A Mathematical Journal Vol.13, N^º03, (17-48). October 2011

 

Applications and Lipschitz results of Approximation by Smooth Picard and Gauss-Weierstrass Type Singular Integrals

 

Razvan A. Mezei

The University of Memphis, Department of Mathematical Sciences, Memphis, TN 38152, U.S.A. email: rmezei@memphis.edu

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ABSTRACT

We continue our studies in higher order uniform convergence with rates and in L_p convergence with rates. Namely, in this article we establish some Lipschitz type results for the smooth Picard type singular integral operators and for the smooth Gauss-Weierstrass type singular integral operators.

Keywords:

Smooth Picard Type singular integral, Smooth Gauss-Weierstrass Type singular integral, modulus of smoothness, rate of convergence, Lp convergence, Higher Order Uniform Convergence with Rates, sharp inequality, Lipschitz functions.

Mathematics Subject Classification: 26A15, 26D15, 41A17, 41A35, 41A60, 41A80.

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RESUMEN

Continuamos nuestros estudios sobre convergencia uniforme de orden superior con radios y sobre convergencia L_p con radios. Concretamente, en este artículo establecemos algunos resultados de tipo Lipschitz para operadores integrales suves del tipo Picard singulares y para operadores integrales singulares de tipo Gauss-Weierstrass.

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References

[1] George A. Anastassiou, "Basic Convergence with Rates of Smooth Picard Singular Operators", J. Comput. Anal. Appl., 8 (2006), 313-334.

[2] George A. Anastassiou, "Lp convergence with rates of smooth Picard singular operators", Differential & difference equations and applications, Hindawi Publ. Corp., New York, (2006), 31-45.

[3] George A. Anastassiou, Razvan A. Mezei, "Uniform Convergence with Rates of Smooth Gauss-Weierstrass Singular Integral Operators", Applicable Analysis, 88:7 (2009), 1015 - 1037.

[4] George A. Anastassiou, Razvan A. Mezei, "Lp Convergence with Rates of Smooth Gauss-Weierstrass Singular Operators", Nonlinear Studies, accepted 2009.

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Received: September 2009. Revised: July 2010.