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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 355, Pages 219–236 (Mi znsl1709)  

This article is cited in 1 scientific paper (total in 1 paper)

On the definition of $B$-points

P. A. Mozolyako

Saint-Petersburg State University
Full-text PDF (290 kB) Citations (1)
References:
Abstract: This paper is devoted to the study of the so-called Bourgain points ($B$-points) of functions in $L^\infty(\mathbb R)$. In 1993, Bourgain showed that for real-valued bounded function $f$ the set $E_f$ of $B$-points is everywhere dense and has maximal Hausdorff dimension, $\dim_H(E_f)=1$; also the vertical variation of the harmonic extension of $f$ to the upper half-plane is finite at $B$-points. An essentially simpler definition of $B$-points is given compared with the original works by Bourgain. A geometric characterization of the $B$-points of Cantor-like sets is obtained. Bibl. – 7 titles.
Received: 23.04.2008
English version:
Journal of Mathematical Sciences (New York), 2009, Volume 156, Issue 5, Pages 845–854
DOI: https://doi.org/10.1007/s10958-009-9289-2
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: P. A. Mozolyako, “On the definition of $B$-points”, Investigations on linear operators and function theory. Part 36, Zap. Nauchn. Sem. POMI, 355, POMI, St. Petersburg, 2008, 219–236; J. Math. Sci. (N. Y.), 156:5 (2009), 845–854
Citation in format AMSBIB
\Bibitem{Moz08}
\by P.~A.~Mozolyako
\paper On the definition of $B$-points
\inbook Investigations on linear operators and function theory. Part~36
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 355
\pages 219--236
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1709}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 156
\issue 5
\pages 845--854
\crossref{https://doi.org/10.1007/s10958-009-9289-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65049083860}
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  • https://www.mathnet.ru/eng/znsl/v355/p219
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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    Full-text PDF :79
    References:41
     
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