Monotonicity and rotundity of Lorentz spaces Γp, w

被引：18

作者：

Ciesielski, Maciej ^{[1
]}

Kaminska, Anna ^{[2
]}

Kolwicz, Pawel ^{[1
]}

Pluciennik, Ryszard ^{[1
]}

机构：

[1] Poznan Tech Univ, Inst Math, PL-60965 Poznan, Poland

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 05期

关键词：

Lorentz spaces; Uniform monotonicity; Lower uniform monotonicity; Strict monotonicity; Rotundity; CALDERON-LOZANOVSKII SPACES; MUSIELAK-ORLICZ SPACES; BANACH-LATTICES; UNIFORM ROTUNDITY; APPROXIMATION; CONVEXITY; CONCAVITY;

D O I：

10.1016/j.na.2011.11.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Criteria for rotundity, strict monotonicity, and lower local uniform monotonicity of the Lorentz spaces Gamma(p, w) of maximal functions are given under arbitrary nonnegative weight function w. Necessary conditions are also established for uniform monotonicity of the spaces G(p, w) for 1 <= p <= infinity. Moreover, the spaces Gamma(1, w) that are uniformly monotone are characterized. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2713 / 2723

页数：11

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