On translation and dilation invariant subspaces of L p (ℝn), 0 < p < 1

被引：0
|
作者：
Aleksandrov A.B. [1 ]
机构：
[1] St.Petersburg Department, Steklov Mathematical Institute, St.Petersburg
来源：
Journal of Mathematical Sciences | 2008年 / 148卷 / 6期
基金：
俄罗斯基础研究基金会;
关键词：
Compact Subset; Lebesgue Measure; Invariant Subspace; Linear Hull; Hardy Class;
D O I：
10.1007/s10958-008-0025-0
中图分类号：
学科分类号：
摘要：
We prove that each translation and dilation invariant subspace X ⊂ L p (n), X ≠ L p (ℝn), is contained in a maximal translation and dilation invariant subspace of L p (ℝn). Moreover, we prove that the set of all maximal translation and dilation invariant subspaces of L p (ℝn) has the power of continuum. Bibliography: 6 titles. © 2008 Springer Science+Business Media, Inc.
引用
收藏
页码：785 / 794
页数：9
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