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

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

引用次数: 0

Abstract

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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论任意滤波的马廷格尔 $$SL^\infty$ 空间乘数

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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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

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