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On the definition of Bourgain points. / Mozolyako, P. A.

в: Journal of Mathematical Sciences , Том 156, № 5, 01.02.2009, стр. 845-854.

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Harvard

Mozolyako, PA 2009, 'On the definition of Bourgain points', Journal of Mathematical Sciences , Том. 156, № 5, стр. 845-854. https://doi.org/10.1007/s10958-009-9289-2

APA

Mozolyako, P. A. (2009). On the definition of Bourgain points. Journal of Mathematical Sciences , 156(5), 845-854. https://doi.org/10.1007/s10958-009-9289-2

Vancouver

Mozolyako PA. On the definition of Bourgain points. Journal of Mathematical Sciences . 2009 Февр. 1;156(5):845-854. https://doi.org/10.1007/s10958-009-9289-2

Author

Mozolyako, P. A. / On the definition of Bourgain points. в: Journal of Mathematical Sciences . 2009 ; Том 156, № 5. стр. 845-854.

BibTeX

@article{1fdbd5232a544cc8b9a2af4bcaa24895,
title = "On the definition of Bourgain points",
abstract = "This paper is devoted to study of the so-called Bourgain points (B-points) for functions from L∞. In 1993, Bourgain showed that for a real-valued bounded function f, the set Ef of B-points is everywhere dense and has the maximal Hausdorff dimension, dim H(Ef ) = 1; in addition, the vertical variation of the harmotic extension of f to the upper half-plane is finite at B-points. An essentially simpler definition of B-points is given compared to that in the original works by Bourgain. A geometric characterization of B-points for Cantor-like sets is obtained. Bibliography: 7 titles. {\textcopyright} 2009 Springer Science+Business Media, Inc.",
author = "Mozolyako, {P. A.}",
year = "2009",
month = feb,
day = "1",
doi = "10.1007/s10958-009-9289-2",
language = "English",
volume = "156",
pages = "845--854",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - On the definition of Bourgain points

AU - Mozolyako, P. A.

PY - 2009/2/1

Y1 - 2009/2/1

N2 - This paper is devoted to study of the so-called Bourgain points (B-points) for functions from L∞. In 1993, Bourgain showed that for a real-valued bounded function f, the set Ef of B-points is everywhere dense and has the maximal Hausdorff dimension, dim H(Ef ) = 1; in addition, the vertical variation of the harmotic extension of f to the upper half-plane is finite at B-points. An essentially simpler definition of B-points is given compared to that in the original works by Bourgain. A geometric characterization of B-points for Cantor-like sets is obtained. Bibliography: 7 titles. © 2009 Springer Science+Business Media, Inc.

AB - This paper is devoted to study of the so-called Bourgain points (B-points) for functions from L∞. In 1993, Bourgain showed that for a real-valued bounded function f, the set Ef of B-points is everywhere dense and has the maximal Hausdorff dimension, dim H(Ef ) = 1; in addition, the vertical variation of the harmotic extension of f to the upper half-plane is finite at B-points. An essentially simpler definition of B-points is given compared to that in the original works by Bourgain. A geometric characterization of B-points for Cantor-like sets is obtained. Bibliography: 7 titles. © 2009 Springer Science+Business Media, Inc.

UR - http://www.scopus.com/inward/record.url?scp=65049083860&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9289-2

DO - 10.1007/s10958-009-9289-2

M3 - Article

AN - SCOPUS:65049083860

VL - 156

SP - 845

EP - 854

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 119109682