Sequences of composition operators in spaces of functions of bounded Φ-variation
Олег Евгеньевич Галкин · Mathematical Notes · 2009
The main results of the paper are contained in Theorems 1 and 2. Theorem 1 presents necessary and sufficient conditions for a sequence of functions h n : 〈c, d〉 → 〈a, b〉, n = 1, 2, ..., to have bounded sequences of Ψ-variations {V Ψ (〈c, d〉; f ◦ h n )} =1 ∞ evaluated for the compositions of an arbitrary function f: 〈a, b〉 → ℝ with finite Φ-variation and the functions h n . In Theorem 2, the same is done for a sequence of functions h n : ℝ → ℝ, n = 1, 2, ..., and the sequence of Ψ-variations {V Ψ(〈a, b〉; h n ◦ f)} =1 ∞ .