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- Title
Sequences of composition operators in spaces of functions of bounded Φ-variation.
- Authors
Galkin, O.
- Abstract
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 { VΨ (〈 c, d〉; f ◦ h n)} 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 { VΨ(〈 a, b〉; h n ◦ f)}.
- Subjects
COMPOSITION operators; LIPSCHITZ spaces; FUNCTIONS of bounded variation; MATHEMATICAL sequences; CONTINUITY
- Publication
Mathematical Notes, 2009, Vol 85, Issue 3/4, p328
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434609030031