Some Generalizations of the Notion of Bounded Variation

Relations between Schramm spaces and generalized Wiener classes

“…A natural and important problem is to determine relations between the above-mentioned classes; see [21], [12], [4], [9], [6], [13], [8] and [5] for some results in this direction. In particular, Perlman and Waterman found the fundamental characterization of embeddings between ΛBV classes in [12].…”

Properties of Functions in the Wiener ClassBVp[a,b]for0<p<Niu1, Wang2 2015Journal of Function Spaces0000View full textAdd to dashboardCite

“…There are many other generalizations of , such as bounded Φ-variation in the sense of Young (see [1]) and Waterman's Λ-bounded variation (see [2]). The class and generalizations of have been studied mainly because of their applicability to the theory of Fourier series and some good approximative properties (see, e.g., [1][2][3][4][5][6][7]).…”

“…[ , ] is a Banach space with the norm = | ( )| + (see, e.g., [3]). In the case 0 < < 1, [ , ] is no longer a Banach space and has not been studied as far as we know.…”

On functions of bounded Λ-variation and integral smoothness

“…In connection to (1.3), we mention that embeddings between ΛBV and other spaces of functions of generalized bounded variation were previously studied in, e.g., [1,2,11,13].…”