On the (C,1)(C,1) summability method of improper integrals

In this paper we prove a Tauberian-like theorem to retrieve the slow oscillation of a real-valued function s(x)s(x) from its (C,1)(C,1) summability of the generator sequence v(x)v(x) and one-sidedly boundedness of the general control modulo of integer order m⩾1m⩾1 with respect to a function satisfying an appropriate condition.