Convergence of Singular Integral Operators in Weighted Lebesgue Spaces

Mine Menekse Yilmaz, Gümrah Uysal

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 􀀀 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.

Keywords


Generalized Lebesgue point, Weighted pointwise convergence, Rate of convergence

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