Ultrasymmetric Orlicz spaces

被引：7

作者：

Astashkin, Sergei V. ^{[2
]}

Maligranda, Lech ^{[1
]}

机构：

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

[2] Samara State Univ, Dept Math & Mech, Samara 443011, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 347卷 / 01期

关键词：

rearrangement invariant spaces; fundamental function; Boyd indices; ultrasymmetric rearrangement invariant spaces; Lorentz spaces; Marcinkiewicz spaces; Orlicz spaces; Lorentz-Orlicz spaces; interpolation of operators;

D O I：

10.1016/j.jmaa.2008.05.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved that ultrasymmetric reflexive Orlicz spaces can be described exactly as all those Orlicz spaces which can be written as some Lorentz spaces. This description is an answer to the problem posed by Pustyinik in [E. Pustylnik, Ultrasymmetric spaces, J. London Math. Soc. (2) 68 (1) (2003) 165-182]. On the other hand, the Lorentz-Orlicz spaces with non-trivial indices of their fundamental functions are ultrasymmetric. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：273 / 285

页数：13

共 27 条

[11] ORLICZ SEQUENCE SPACES .3.
LINDENSTRAUSS, J
TZAFRIRI, L
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1973, 14 (04) : 368 - 389
[12] Lindenstrauss J., 1979, ERGEB MATH GRENZGEB, V97
[13] LINDENSTRAUSS J, 1977, CLASSICAL BANACH SPA, V1
[14] Lorentz G. G., 1961, P AM MATH SOC, V12, P127, DOI 10.1090/S0002-9939-1961-0123182-3
[15] Lorentz GG., 1951, Pacific J. Math., V1, P411, DOI [10.2140/pjm.1951.1.411, DOI 10.2140/PJM.1951.1.411]
[16] Maligranda L., 1985, Dissertationes Math. (Rozprawy Mat.), V234, P49
[17] Maligranda L, 1989, SEMINARIOS MATEMATIC, V5
[18] MONTGOMERYSMITH SJ, 1992, STUD MATH, V103, P161
[19] NOVIKOV IY, 1988, MEASURE INTEGRAL INT, P62
[20] NOVIKOV IY, 1983, SIB MAT ZH, V24, P193

← 1 2 3 →