Decomposition of convex additively slowly varying functions

Abstract

We find conditions which imply that the difference of two slowly varying functions is slowly varying. Given an additively slowly varying increasing convex function l, we consider the class K l of increasing functions F such that F/l is increasing convex. If an additively slowly varying function L belongs to K l , we find conditions under which, if we decompose L into a sum L = F + G, where F, G ∈ K l , then it follows that F and G are necessarily slowly varying. As an auxiliary result, we find some properties of additively slowly varying functions with remainder term which are also of independent interest.