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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 355, Pages 219–236
(Mi znsl1709)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/znsl1709 https://www.mathnet.ru/eng/znsl/v355/p219
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