on ‎i‎nclusion relations between generalized wiener classes

In this paper we aim to study inclusion relations between the generalized wiener classes λbv(pn↑p) . in particular, we give a sufficient condition for the inclusion λbv(pn↑p) ⊆ γbv(qn↑q) which leads us to new results for other classes of functions previously considered. we also obtain a necessary and sucient condition for equality of two distinct classes of this type. furthermore, we extend and unify a number of results in the literature including an important theorem of avdispahic about waterman spaces.