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

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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://www.ejpam.com/index.php/ejpam/article/view/2507