Rademacher functions in Cesàro type spaces

Sergei V. Astashkin ; Lech Maligranda

Studia Mathematica, Tome 196 (2010), p. 235-247 / Harvested from The Polish Digital Mathematics Library

Résumé

The Rademacher sums are investigated in the Cesàro spaces $Ces_{p}$ (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces $K_{p,w}$ on [0,1]. They span l₂ space in $Ces_{p}$ for any 1 ≤ p < ∞ and in $K_{p,w}$ if and only if the weight w is larger than $t log₂^{p/2}(2/t)$ on (0,1). Moreover, the span of the Rademachers is not complemented in $Ces_{p}$ for any 1 ≤ p < ∞ 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 l₂, this span is a complemented subspace in $K_{p,w}$.

Détail

Publié le : 2010-01-01

Zbl 1202.46031

EUDML-ID : urn:eudml:doc:285406