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Some convergence results for nonlinear singular integral operators

Karsli H.

Demonstratio Mathematica

2013

Vol. 46, nr 4

729--740

In this paper, we establish some pointwise convergence results for a family of certain nonlinear singular integral operators Tλf of the form (...), acting on functions with bounded (Jordan) variation on an interval [a, b] as λ→λ0. Here, the kernels (...) satisfy some suitable singularity assumptions. We remark that the present study is a continuation and extension of the study of pointwise approximation of the family of nonlinear singular integral operators (1) begun in [18].

Nonlinear singular integrals depending on two parametres

Świderski T., Wachnicki E.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2000

[Z] 40

181-189