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

Abstract

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.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.

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