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arXiv math/9408208math.FA
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原子弱L^p空间的同构分类

Isomorphic classification of atomic weak L^p spaces

Denny H. Leung

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摘要：

设$\msp$是一个测度空间，令$1 < p < \infty$ . { \em弱$L^p$ }\/空间$\wlp$由所有可测函数$f$组成，使得\[ \|f\| = \sup_{t>0}t^{\frac{1}{p}}f^*(t) < \infty,\]，其中$f^*$是$|f|$的递减重排。它是一个在一个范数下的Banach空间，这个范数等价于上面的表达式。本文研究了当$\msp$是纯原子时弱$L^p$空间的同构分类问题。本文还证明了，若$\msp$是可数生成的$σ$ -有限测度空间，则$\wlp$（无限维）必同构于$\ell^\infty$或$\seq$ .这篇文章的结果于1994年5月在密苏里州哥伦比亚市的会议上发表。

英文摘要：

Let $\msp$ be a measure space and let $1 < p < \infty$. The {\em weak $L^p$}\/ space $\wlp$ consists of all measurable functions $f$ such that \[ \|f\| = \sup_{t>0}t^{\frac{1}{p}}f^*(t) < \infty,\] where $f^*$ is the decreasing rearrangement of $|f|$. It is a Banach space under a norm which is equivalent to the expression above. In this paper, we pursue the problem of classifying weak $L^p$ spaces isomorphically when $\msp$ is purely atomic. It is also shown that if $\msp$ is a countably generated $σ$-finite measure space, then $\wlp$ (if infinite dimensional) must be isomorphic to either $\ell^\infty$ or $\seq$. The results of this article were presented at the conference in Columbia, Missouri in May, 1994.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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