有限希尔伯特变换的度量论问题

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-08-26 DOI:10.1002/mana.202200537

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

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引用次数: 0

摘要

有限希尔伯特变换，当作用于经典齐格蒙德空间 (over ) 时，在 [8] 中进行了深入研究。在本注释中，通过每个 Borel 集合的-值度量，建立了、的积分表示。这种积分表示法，连同 , 的各种非难性质，允许使用度量论方法（[8] 中没有）来建立 . 例如，由于巴拿赫函数空间之间的算子不是有阶的，所以它不是完全连续的，也不是弱紧凑的。适当的 Parseval 公式起着至关重要的作用。

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Measure theoretic aspects of the finite Hilbert transform

The finite Hilbert transform , when acting in the classical Zygmund space (over ), was intensively studied in [8]. In this note, an integral representation of is established via the ‐valued measure for each Borel set . This integral representation, together with various non‐trivial properties of , allows the use of measure theoretic methods (not available in [8]) to establish new properties of . For instance, as an operator between Banach function spaces is not order bounded, it is not completely continuous and neither is it weakly compact. An appropriate Parseval formula for plays a crucial role.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index