Rademacher functions in Cesàro type spaces

Sergei V. Astashkin¹ ; Lech Maligranda²

¹ Department of Mathematics and Mechanics Samara State University Akad. Pavlova 1 443011 Samara, Russia
² Department of Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden

Studia Mathematica, Tome 198 (2010) no. 3, pp. 235-247

Résumé

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 $K_{p,w}$.

Détail

DOI : 10.4064/sm198-3-3

Keywords: rademacher sums investigated ces spaces ces infty weighted korenblyum kre levin spaces span space ces infty only weight larger log moreover span rademachers complemented ces infty quasi concave weight span rademacher functions isomorphic span complemented subspace