In the present paper we study embeddings of some spaces of functions of generalized bounded variation into classes of functions with given majorant of average modulus of continuity introduced by B. Sendov and V. Popov. We consider the spaces ΛBV (p) of functions of bounded (Λ − p)-variation suggested by D. Waterman (for p = 1) and M. Shiba (for p > 1) and spaces V (v(n)) of functions with given majorant of its modulus of variation. The last quantity was introduced by Z. A. Chanturia. The necessary and sufficient conditions of such embeddings are proved.
