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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.13 no.3 Temuco Oct. 2011 

CUBO A Mathematical Journal Vol.13, Nº03, (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:


We continue our studies in higher order uniform convergence with rates and in Lp 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.


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.


Continuamos nuestros estudios sobre convergencia uniforme de orden superior con radios y sobre convergencia Lp 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.


[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.

Received: September 2009. Revised: July 2010.

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