On ‎I‎nclusion Relations Between Generalized Wiener Classes

Subject Areas : International Journal of Industrial Mathematics

ناصر حدادزاده ^{1 *}

1 - Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan, Iran.

Received: 2019-07-05 Accepted : 2019-12-25 Published : 2020-08-01

Keywords: Generalized bounded variation, Waterman class, Modulus of variation, Generalized Wiener class,

Abstract :

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.

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