Rademacher functions in Cesàro type spaces

Sergei V. Astashkin, and Lech Maligranda. "Rademacher functions in Cesàro type spaces." Studia Mathematica 198.3 (2010): 235-247. <http://eudml.org/doc/285406>.

@article{SergeiV2010,
abstract = {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 $K_\{p,w\}$.},
author = {Sergei V. Astashkin, Lech Maligranda},
journal = {Studia Mathematica},
keywords = {Rademacher sums; Cesàro spaces; Korenblyum-Kreĭn-Levin spaces},
language = {eng},
number = {3},
pages = {235-247},
title = {Rademacher functions in Cesàro type spaces},
url = {http://eudml.org/doc/285406},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Sergei V. Astashkin
AU - Lech Maligranda
TI - Rademacher functions in Cesàro type spaces
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 3
SP - 235
EP - 247
AB - 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 $K_{p,w}$.
LA - eng
KW - Rademacher sums; Cesàro spaces; Korenblyum-Kreĭn-Levin spaces
UR - http://eudml.org/doc/285406
ER -