ON A CLASS OF FUNCTIONS OF REGULAR ASYMPTOTIC BEHAVIOR

摘要

Let f the defined for all x≥0 and integrable on every finite interval.nIn the first part of this paper we study the asymptotic properties of f which follow from these hypotheses. If σ≠0 the asymptotic relation (*) implies already that H(λ)=A(λσ-1).nIn the second part of this paper, given a function g, a real number σ and a slowly varying function L, we give necessary and sufficient conditions for the existence of a non decreasing function g* such that the function f = g+g* satisfies the asymptotic relation (*).