Ф-variation and p-variation; Inequalities for Integrals
Let V be the class of all functions Φ: [0,∞) ? [0,∞) which are strictly increasing, continuous, unbounded, and 0 at 0. Let CV be the subclass of convex functions in V. Let X be a Banach space with norm \( \|\cdot\|\), let J be a nonempty interval in R, let f be a function defined on J with values in X, and let Φ ∈ V. Recall that an interval is called nondegenerate if it contains more than one point.
KeywordsBanach Space Point Function Interval Function Concave Function Orlicz Space
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