A note on rate of convergence of double singular integral operators


Yilmaz M. M. , UYSAL G. , İBİKLİ E.

ADVANCES IN DIFFERENCE EQUATIONS, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

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: L-lambda(f; x, y) = integral integral(D) f (s, t) H-lambda (s-x, t-y) ds dt, (x, y) is an element of D, where D = < a, b > x < c, d > (< a, b > x < c, d > is an arbitrary closed, semi-closed or open region in R-2) and lambda epsilon Lambda, Lambda is a set of non-negative numbers with accumulation point lambda(0). Also we provide an example to support these theoretical results.