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 $H^ω\subset Λ BV$, 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 $BV(p(n)\uparrow)$ 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.