… the concept of (p, k)-variation (1 < p < ∞, k ∈ ℕ) of a real function on a … a function u : [a, b]
→ ℝ has bounded (p, k)-variation if and only if u (k−1) is absolutely continuous on [a, b] and u (k…

… A function u E LI(n) whose partial derivatives in the sense of distributions are measures with
… total variation in n is called a function of bounded variation. The class of all such functions …

… in the class merely because its 0 or 41 is non-measurable, we define the extended class
T to consist of those functions f for which k and V/ are respectively dominated by summable …

… convex functions (sce, eg [4, Theorem 1.1]). In the present paper we introduce the concept
of bounded (p,2)-variation (1 5 p < oo) and prove a characterization of the class A:[a,b] (1 < p …

… the concept of bounded p-variation. In order to do that, we introduce a strictly increasing
continuous function α : [a, b] → R. Then, we consider the bounded p-variation with respect to α. …

… If C can be chosen independently of V, then we say that u has boun variation in U, and we
write u € BnV(U; K"). If u G BnVioc(U; IK"), the Riesz Representation Theorem asserts tha is a …

… We say that f is a function of bounded p-variation if … In the case p = 1 Hardy and Littlewood
[11] proved that a function f ∈ L1 is equivalent to a function of bounded variation if and only if …

… is said to be of bo variation if it satisfies the condition of definition V and if in additiont f(x, of
bounded variation in y (ie, k (x) is finite) for at least one x and f(x, bounded variation in x (ie, 4v…

… the total variation measure idul, and we show that BV(Q, E) inherits many classical properties
of real functions with bounded variation. … Hence, we can find a constant K such that 6(x, y) …

… bounded and then relatively compact. Since any open set can be approximated from inside
by closed and bounded … Ω if it holds on every compact set K ⊆ Ω (or equivalently on every …