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On pointwise convergence of bivariate nonlinear singular integral operators
(University of Kuwait, 2017) Uysal, G.; Yilmaz, M.M.; Ibikli, E.
In this paper, we present some theorems on pointwise convergence and the rate of pointwise convergence for the family of nonlinear bivariate singular integral operators of the following form: (EQUATION PRESENTED) where f is a real valued and integrable function on a bounded arbitrary closed, semi-closed or open region D = ?a, b? × ?c, d? in ?2 or D = ?2 and A is the set of non-negative indices with accumulation point ?0.
Some theorems on the approximation of non-integrable functions via singular integral operators
(Jangjeon Research Institute for Mathematical Sciences and Physics, 2015) Uysal, G.; Yilmaz, M.M.
In this paper we study the pointwise approximation of functions which are non-integrable on D =< -?,? > x < -?,? > where ?-?,?? x ?-?,?? is a closed, semi-closed or open region, by double singular integral operators with radial kernels of the form: L?= (f;x,y)= ?Df (s,t)K?(?(s - x)2+(t - y)2)dsdtat generalized Lebesgue point. Also we investigate the rate of convergence of the operators L?(f;x,y) at this point. © 2015, Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.