Dichotomies for Lp spaces

被引：14

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

页码：382 / 390

页数：9