Convergence of Singular Integral Operators in Weighted Lebesgue Spaces

Authors

  • Mine Menekse Yilmaz Gaziantep University
  • Gumrah Uysal Karabuk University Ankara University

Keywords:

Generalized Lebesgue point, Weighted pointwise convergence, Rate of convergence

Abstract

In this paper, the pointwise approximation to functions f 2 L1;w ha; bi by the convo-lution type singular integral operators given in the following form:L (f; x) =Zbaf (t)K (t ô€€€ x) dt; x 2 ha; bi ; 2 R+0where ha; bi stands for arbitrary closed, semi closed or open bounded interval in R, L1;w ha; bidenotes the space of all measurable functions f for whichfwis integrable on ha; bi and w : R ! R+is a corresponding weight function, at a -generalized Lebesgue point and the rate of convergenceat this point are studied.

Author Biography

  • Gumrah Uysal, Karabuk University Ankara University

    Department of Mathematics

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Published

2017-02-03

Issue

Vol. 10 No. 2: (January 2017)

Section

Approximation Theory

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Convergence of Singular Integral Operators in Weighted Lebesgue Spaces. (2017). European Journal of Pure and Applied Mathematics, 10(2), 335-347. https://ejpam.com/index.php/ejpam/article/view/2507