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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2009, Volume 85, Issue 3, Pages 330–341 (Mi mz3891)

Sequences of Composition Operators in Spaces of Functions of Bounded $\Phi$-Variation

O. E. Galkin

N. I. Lobachevski State University of Nizhni Novgorod

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 $h_n\colon\langle c,d\rangle\to\langle a,b\rangle$, $n=1,2,…$, to have bounded sequences of $\Psi$-variations $\{V_\Psi(\langle c,d\rangle;f\circ h_n)\}_{n=1}^\infty$ evaluated for the compositions of an arbitrary function $f\colon\langle a,b\rangle\to\mathbb R$ with finite $\Phi$-variation and the functions $h_n$. In Theorem \ref{t2:u330}, the same is done for a sequence of functions $h_n\colon\mathbb R\to\mathbb R$, $n=1,2,…$, and the sequence of $\Psi$-variations $\{V_\Psi(\langle a,b\rangle;h_n\circ f)\}_{n=1}^\infty$.

Keywords: composition operator, $\varphi$-function, $\Phi$-variation, modulus of continuity, Lipschitz function, Hölder property

DOI: https://doi.org/10.4213/mzm3891

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English version:
Mathematical Notes, 2009, 85:3, 328–339

Bibliographic databases:

UDC: 517.518.24+517.518.3

Citation: O. E. Galkin, “Sequences of Composition Operators in Spaces of Functions of Bounded $\Phi$-Variation”, Mat. Zametki, 85:3 (2009), 330–341; Math. Notes, 85:3 (2009), 328–339

Citation in format AMSBIB
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