Properties of Functions of Generalized Bounded Variations

Inclusions of Waterman–Shiba spaces into generalized Wiener classes

“…When p = 1, ΛBV (p) is the well-known Waterman space ΛBV (see e. g. [25] and [26]). Some of the properties and applications of functions of class ΛBV (p) were discussed in [8], [9], [11], [12], [16], [17], [18], [19], [20], [22], [23] and [24]. ΛBV (p) equipped with the norm f Λ, p := |f (0)| + V (f ) is a Banach space.…”