A THEOREM ON WEIGHTED APPROXIMATION BY SINGULAR INTEGRAL OPERATORS

Abstract

In this paper, pointwise approximation of functions f 2 L1;'(R)by the convolution type singular integral operators given in the following form:$L_(f; x) =ZRf (t)K_ (t 􀀀 x) dt; x 2 R; _ 2 _ _ R+0 ;$is studied. Here, L1;'(R) denotes the space of all measurable functions ffor which $___f'___ $ is integrable on R and ' : R ! R+ is a corresponding weightfunction.