Rademacher functions in BMO

Tom 205 / 2011

Sergey V. Astashkin, Mikhail Leibov, Lech Maligranda Studia Mathematica 205 (2011), 83-100 MSC: 46E30, 46B20, 46B42. DOI: 10.4064/sm205-1-6

Streszczenie

The Rademacher sums are investigated in the $BMO$ space on $[0, 1]$. They span an uncomplemented subspace, in contrast to the dyadic $BMO_d$ space on $[0, 1]$, where they span a complemented subspace isomorphic to $l_2$. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in $BMO$ are studied and an analog of the Kadec–Pełczyński type alternative with $l_2$ and $c_0$ spaces is proved.

Autorzy

  • Sergey V. AstashkinDepartment of Mathematics and Mechanics
    Samara State University
    Akad. Pavlova 1
    443011 Samara, Russia
    e-mail
  • Mikhail LeibovHorton Point LLC
    1180 Avenue of the Americas
    New York, NY 10036, U.S.A.
    e-mail
  • Lech MaligrandaDepartment of Engineering Sciences and Mathematics
    Luleå University of Technology
    SE-971 87 Luleå, Sweden
    e-mail

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