On ‎I‎nclusion Relations Between Generalized Wiener Classes

We studied inclusion relations between the generalized Wiener classes. In particular, we give a sufficient condition for the inclusion ΛBV^(p_n↑p) ⊆ ΓBV^(q_n↑q) which leads us to new results for such spaces. We also obtain a necessary and sufficient 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 Avdispahić about Waterman spaces.