RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

Full text: PDF file (496 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.518.24+517.518.3
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

Citation in format AMSBIB
\Bibitem{Gal09}
\by O.~E.~Galkin
\paper Sequences of Composition Operators in Spaces of Functions of Bounded $\Phi$-Variation
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 3
\pages 330--341
\mathnet{http://mi.mathnet.ru/mz3891}
\crossref{https://doi.org/10.4213/mzm3891}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2548041}
\zmath{https://zbmath.org/?q=an:1194.47025}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 3
\pages 328--339
\crossref{https://doi.org/10.1134/S0001434609030031}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266561100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949181183}


Linking options:
  • http://mi.mathnet.ru/eng/mz3891
  • https://doi.org/10.4213/mzm3891
  • http://mi.mathnet.ru/eng/mz/v85/i3/p330

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:279
    Full text:86
    References:31
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020