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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 2, Pages 3–20 (Mi izv69)  

This article is cited in 4 scientific papers (total in 4 papers)

Estimates for a uniform modulus of continuity of functions from symmetric spaces

E. I. Berezhnoi

Yaroslavl State University

Abstract: We prove a multidimensional “correctability” theorem of the Oskolkov type for a function given in $\mathbb R^n$ whereby a sharp quantitative estimate for the uniform modulus of continuity of a function on “large” sets is given if an estimate of the modulus of continuity of this function in a symmetric space is known. We show that an estimate of a uniform modulus of continuity depends only on the eigenfunction of the symmetric space.

DOI: https://doi.org/10.4213/im69

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English version:
Izvestiya: Mathematics, 1996, 60:2, 231–248

Bibliographic databases:

UDC: 517.5
MSC: 26A15, 46E30
Received: 14.04.1992

Citation: E. I. Berezhnoi, “Estimates for a uniform modulus of continuity of functions from symmetric spaces”, Izv. RAN. Ser. Mat., 60:2 (1996), 3–20; Izv. Math., 60:2 (1996), 231–248

Citation in format AMSBIB
\Bibitem{Ber96}
\by E.~I.~Berezhnoi
\paper Estimates for a~uniform modulus of continuity of functions from symmetric spaces
\jour Izv. RAN. Ser. Mat.
\yr 1996
\vol 60
\issue 2
\pages 3--20
\mathnet{http://mi.mathnet.ru/izv69}
\crossref{https://doi.org/10.4213/im69}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1399416}
\zmath{https://zbmath.org/?q=an:0906.26005}
\transl
\jour Izv. Math.
\yr 1996
\vol 60
\issue 2
\pages 231--248
\crossref{https://doi.org/10.1070/IM1996v060n02ABEH000069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746937282}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. I. Berezhnoi, “The Correction Theorem for Anisotropic Spaces”, Math. Notes, 70:3 (2001), 291–299  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. I. Berezhnoi, “A Subspace of Hölder Space Consisting Only of Nonsmoothest Functions”, Math. Notes, 74:3 (2003), 316–325  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. E. I. Berezhnoǐ, “A sharp extrapolation theorem for Lorentz spaces”, Siberian Math. J., 54:3 (2013), 406–418  mathnet  crossref  mathscinet  isi
    4. E. I. Berezhnoi, “Correction theorem for Sobolev spaces constructed by a symmetric space”, Proc. Steklov Inst. Math., 284 (2014), 32–49  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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