Convolution functions of several variables with generalized bounded variation

Inclusion of $ΛBV^{(p)}$ spaces in the classes $H_ω^{q}$

“…Some of the basic properties of functions of class ΛBV (p) were discussed by R. G. Vyas in [12] recently. More results concerned with the Waterman-Shiba classes and their applications can be found in [1], [2], [4], [6], [7], [8], [10] and [11]. ΛBV (p) equipped with the norm f Λ,…”

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.…”