Lipschitz-Hölder空间中的对偶性和距离公式

IF 0.6 4区 数学 Q3 MATHEMATICS
Francesca Angrisani, G. Ascione, Luigi d’Onofrio, Gianluigi Manzo
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引用次数: 8

摘要

对于紧致度量空间$(K,\rho)$,$Lip(K,\lho)$的前对偶可以用配备有Kantorovich-Rubinstein范数的$K$上的有限(有符号)Borel测度的赋范空间$M(K)$来识别,这是由于Kantorovich[20]。在这里,我们通过[10]中的一些结果推导出$M(K)$的原子分解。在适当的假设下,$Lip(K,\rho)$和$(Lip(K,\ rho))_{**}$[15]之间存在自然等距同构。在这项工作中,我们还证明了对$(lip(K,\rho),lip(K,\ rho))$可以在K.M.Perfekt引入的o-o型结构理论中建立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Duality and distance formulas in Lipschitz–Hölder spaces
For a compact metric space $(K, \rho)$, the predual of $Lip(K, \rho)$ can be identified with the normed space $M(K)$ of finite (signed) Borel measures on $K$ equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of $M(K)$ by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between $Lip(K, \rho)$ and $(lip(K, \rho))_{**}$ [15]. In this work we also show that the pair $(lip(K, \rho), Lip(K, \rho))$ can be framed in the theory of o-O type structures introduced by K. M. Perfekt.
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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