Rademacher functions in Cesàro type spaces

Tom 198 / 2010

Sergei V. Astashkin, Lech Maligranda Studia Mathematica 198 (2010), 235-247 MSC: 46E30, 46B20, 46B42. DOI: 10.4064/sm198-3-3

Streszczenie

The Rademacher sums are investigated in the Cesàro spaces ${\rm Ces}_p$ $(1\le p\le \infty)$ and in the weighted Korenblyum–Kre\uın–Levin spaces $K_{p, w}$ on $[0, 1]$. They span $l_2$ space in ${\rm Ces}_p$ for any $1\le p< \infty$ and in $K_{p, w}$ if and only if the weight $w$ is larger than $t \log_2^{p/2} ({2}/{t})$ on $(0, 1)$. Moreover, the span of the Rademachers is not complemented in ${\rm Ces}_p$ for any $1\le p< \infty$ or in $K_{1, w}$ for any quasi-concave weight $w$. In the case when $p > 1$ and when $w$ is such that the span of the Rademacher functions is isomorphic to $l_2$, this span is a complemented subspace in $K_{p,w}$.

Autorzy

  • Sergei V. AstashkinDepartment of Mathematics and Mechanics
    Samara State University
    Akad. Pavlova 1
    443011 Samara, Russia
    e-mail
  • Lech MaligrandaDepartment of Mathematics
    Luleå University of Technology
    SE-971 87 Luleå, Sweden
    e-mail

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