A THEOREM ON WEIGHTED APPROXIMATION BY SINGULAR INTEGRAL OPERATORS

In this paper, pointwise approximation of functions f ∈ L1,φ(R) by the convolution type singular integral operators given in the following form: Lλ(f ;x) = ∫ R f (t)Kλ (t− x) dt, x ∈ R, λ ∈ Λ ⊂ R+0 , is studied. Here, L1,φ(R) denotes the space of all measurable functions f for which ∣∣∣ f φ ∣∣∣ is integrable on R and φ : R → R+ is a corresponding weight function.