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This article is cited in 1 scientific paper (total in 1 paper)
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 $h_n\colon\langle c,d\rangle\to\langle a,b\rangle$, $n=1,2,\dots$, 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 $h_n\colon\mathbb R\to\mathbb R$, $n=1,2,\dots$, 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.
Received: 26.06.2007
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
Linking options:
https://www.mathnet.ru/eng/mzm3891https://doi.org/10.4213/mzm3891 https://www.mathnet.ru/eng/mzm/v85/i3/p330
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