Approximation properties of a modified Gauss–Weierstrass singular integral in a weighted space

Abstract Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space L^p, w L p, w, define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function f L^p, w f ∈ L p, w. We use the modulus of continuity of the functions to measure the rate of convergence.