Rademacher functions in Morrey spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Astashkin, Sergei V.^1,2  Maligranda, Lech³ 

[1] Samara State Univ, Dept Math & Mech, Acad Pavlova 1, Samara 443011, Russia

[2] SSAU, Moskovskoye Shosse 34, Samara 443086, Russia

[3] Lulea Univ Technol, Dept Math, SE-97187 Lulea, Sweden

关键词: Rademacher functions;    IViorrey spaces;    Korenblyum-Krein-Levin spaces;    Marcinkiewicz spaces;    Complemented subspaces;   

DOI  :  10.1016/j.jmaa.2016.07.008

来源: Elsevier

【 摘 要 】

The Rademacher sums are investigated in the Morrey spaces M-p,M-w on [0,1] for 1 <= p < infinity and weight w being a quasi-concave function. They span l(2) space in M-p,M-w if and only if the weight w is smaller than log(2)(-1/2) 2/t on (0,1). Moreover, if 1 < p < infinity the Rademacher subspace R-p,R-w is complemented in M-p,M-w if and only if it is isomorphic to l(2). However, the Rademacher subspace R-1,R-w is not complemented in M-1,M-w for any quasi-concave weight w. In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces M-p,M-w is described. It turns out that for any infinite-dimensional subspace X of R-p,R-w the following alternative holds: either X is isomorphic to l(2) or X contains a subspace which is isomorphic to c(0) and is complemented in R-p,R-w. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free