A note on rate of convergence of double singular integral operators

被引：0
|
作者：
Mine Menekse Yilmaz
Gumrah Uysal
Ertan Ibikli
机构：
[1] Gaziantep University,Department of Mathematics, Faculty of Arts and Science
[2] Karabuk University,Department of Mathematics, Faculty of Science
[3] Ankara University,Department of Mathematics, Faculty of Science
来源：
Advances in Difference Equations | / 2014卷
关键词：
-generalized Lebesgue point; radial kernel; pointwise convergence; rate of convergence;
D O I：
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摘要：
In this paper we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators with radial kernel in two-dimensional setting in the following form: Lλ(f;x,y)=∬Df(s,t)Hλ(s−x,t−y)dsdt, (x,y)∈D, where D=〈a,b〉×〈c,d〉 (〈a,b〉×〈c,d〉 is an arbitrary closed, semi-closed or open region in R2) and λ∈Λ, Λ is a set of non-negative numbers with accumulation point λ0. Also we provide an example to support these theoretical results.
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