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On convergence and rate of convergence of nonlinear singular integral operators

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Let G be a locally compact abelian group with the Haar measure. In the present paper we investigate both the pointwise convergence and the rate of convergence of the nonlinear integral operators, to a continuous and Lebesgue point of f 2 L1(a; b) as (x; ) ! (x0; 0).

Abstract

Let G be a locally compact abelian group with the Haar measure. In the present paper we investigate both the pointwise convergence and the rate of convergence of the nonlinear integral operators, to a continuous and Lebesgue point of f 2 L1(a; b) as (x; ) ! (x0; 0).

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