O-Regularly Varying Functions and Strong Asymptotic Equivalence

In this paper we prove that in the class of all measurable positive functions defined on the interval wa,q`. a)0., the class of functions which preserve the strong asymptotic equivalence on the set of functions x: wa,q`.¬Rq, x t.ª q`, tªq`4, is a class of O-regularly varying functions with continuous index function. We also prove a representation theorem for functions from this class.