Convex additively slowly varying functions

We study the problem of subtraction of slowly varying functions. It is well-known that the difference of two slowly varying functions need not be slowly varying and we look for some additional conditions which guarantee the slow variation of the difference. To this end we consider all possible decompositions L = F +G of a given increasing convex additively slowly varying function L into a sum of two increasing convex functions F and G.We characterize the class of functions L for which in every such decomposition the summands are necessarily additively slowly varying. The class O + 2 we obtain is related to the well-known class O g where, instead of first order differences as in O g, we have second order differences.  2002 Elsevier Science (USA). All rights reserved.