The property of good decomposition in Hardy fields (Q1777556)

A hindrance in some applications of Karamata class of regularly varying functions is the fact that these do not form a field with respect to the usual pointwise aadition and multiplication of such functions (the difference in general does not belong to the class). By continuing their previous investigation the authors define some subsets of the considered class which do form a field. We quote here, as an example, a result from the paper: If the difference of two regularly varying functions belonging to a Hardy field is positive and bounded away from zero, then it is regularly varying.