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

页码：785 / 794

页数：9

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On translation and dilation invariant subspaces of L p (ℝn), 0 &lt; p &lt; 1

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