论任意滤波的马廷格尔 $$SL^\infty$ 空间乘数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-21 DOI:10.1007/s00209-024-03494-9

Anton Tselishchev

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引用次数: 0

摘要

在本文中，我们将研究以下问题：对于滤波概率空间上的给定有界正函数 f，我们能否找到另一个函数（乘数）m，使得函数 mf 不是 "太小"，而是其平方函数是有界的？我们明确地展示了如何为通常的马丁格尔平方函数和所谓的条件平方函数构造这样的乘数。此外，我们还证明，对于通常的平方函数，可以应用基斯利亚科夫（Kislyakov）的非构造性抽象修正定理，得到更一般的说明。

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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On multipliers into martingale $$SL^\infty $$ spaces for arbitrary filtrations

In this paper we study the following problem: for a given bounded positive function f on a filtered probability space can we find another function (a multiplier) m, $0\le m\le 1$, such that the function mf is not “too small” but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function. Besides that, we show that for the usual square function more general statement can be obtained by application of a non-constructive abstract correction theorem by Kislyakov.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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