Dichotomies for Lp spaces

被引：13
|
作者：
Glab, Szymon [1 ]
Strobin, Filip [1 ,2 ]
机构：
[1] Tech Univ Lodz, Inst Math, PL-93005 Lodz, Poland
[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 368卷 / 01期
关键词：
Measure space; L-p space; Porous sets; Porosity;
D O I：
10.1016/j.jmaa.2010.02.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Assume that (X, Sigma, mu) is a measure space and p(1), . . . , p(n), r > 0. We prove that {(f(1), . . . , f(n)) is an element of L-p1 x . . . x L-pn; f(1) . . . f(n) is an element of L-r} is either L-p1 x . . . x L-pn or a sigma-porous subset of L-p1 x . . . x L-pn. This dichotomy depends on properties of mu and the sign of the number 1/r - 1/p(1) - . . . - 1/p(n). (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：382 / 390
页数：9
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