An Embedding Theorem given by the Modulus of Variation - Leindler, Laszlo (Journal of Informatics and Mathematical Sciences, 2009)
In [5] and [6] we extended an interesting theorem of Medvedeva [7] pertaining to the embedding relation H^ωΛ BV, where Λ BV denotes the set of functions of Λ-bounded variation. Our theorem proved in [6] unifies the notion of φ-variation due to Young [8] and that of the generalized Wiener class BV(p(n)) due to Kita and Yoneda [4]. In this note we generalize the theorem proved in [6] such that it will use the concept of the modulus of variation due to Chanturia [2]. For further references pertaining to the new notion mentioned above we refer to an interesting paper by Goginava and Tskhadaia [3]. We also show that our new theorem includes our previous result as a special case.