An Embedding Theorem given by the Modulus of Variation

Laszlo Leindler


In [5] and [6] we extended an interesting theorem of Medvedeva [7] pertaining to the embedding relation $H^\omega\subset \Lambda BV$, where $\Lambda BV$
denotes the set of functions of $\Lambda$-bounded variation. Our theorem proved in [6] unifies the notion of $\varphi$-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.


Embedding relation; Bounded variation; Modulus of variation; Continuity

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