双迭代外$L^p$空间的对偶性

IF 0.7 3区 数学 Q2 MATHEMATICS
Marco Fraccaroli
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引用次数: 1

摘要

我们研究了二重迭代的外L空间,即与三个指数相关并定义在具有一个测度和两个外测度的集合上的外L。我们证明了在有限集的情况下,在外测度之间的某些条件下,双迭代外L空间在集的基数上一致同构于Banach空间。我们通过展示它们之间预期的对偶性质来实现这一点。我们还提供了反例,证明了均匀性在有限集上的任何任意设置中都不成立,至少在一定的指数范围内是不成立的。我们证明了在Uraltsev描述的上半3-空间无限集中Banach空间的同构性和双迭代外L空间之间的对偶性质,超越了有限集的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Duality for double iterated outer $L^p$ spaces
We study the double iterated outer L spaces, namely the outer L spaces associated with three exponents and defined on sets endowed with a measure and two outer measures. We prove that in the case of finite sets, under certain conditions between the outer measures, the double iterated outer L spaces are isomorphic to Banach spaces uniformly in the cardinality of the set. We achieve this by showing the expected duality properties between them. We also provide counterexamples demonstrating that the uniformity does not hold in any arbitrary setting on finite sets, at least in a certain range of exponents. We prove the isomorphism to Banach spaces and the duality properties between the double iterated outer L spaces also in the upper half 3-space infinite setting described by Uraltsev, going beyond the case of finite sets.
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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