Paatero’s V(k) space II

IF 0.3 Q4 MATHEMATICS
Valentin V. Andreev, Miron B. Bekker, Joseph A. Cima
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引用次数: 0

Abstract

Abstract In this article we continue our investigation of the Paatero space. We prove that the intersection of every Paatero class V(k) with every Hardy space Hp is closed in that Hp and associate singular continuous measures to elements of V(k). There have been no examples in the literature of functions in V(k) with zeros in the unit disk other than the one at the origin. We close this gap in the literature. We derive a representation of the measure associated to a function in V(k) for functions whose derivatives are rational, or algebraic, or transcendental functions in the unit disk.Finally, we consider the notion of regulated domains, introduced by Pommerenke and show that there are regulated domains whose boundary is not of bounded boundary rotation.
帕特罗的V(k)空间II
在本文中,我们继续研究Paatero空间。证明了每一个Paatero类V(k)与每一个Hardy空间Hp的交是闭的,即Hp与V(k)的元素的奇异连续测度相关联。在文献中,除了原点上的函数外,还没有在单位圆盘上的函数为零的例子。我们在文献中填补了这个空白。我们在V(k)中推导出与函数相关的测度的表示,这些函数的导数是单位圆盘上的有理函数、代数函数或超越函数。最后,我们考虑了由Pommerenke引入的调节域的概念,并证明了存在边界不具有有界边界旋转的调节域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
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