关于迭代旁积的泰勒估计的说明

arXiv - MATH - Probability Pub Date : 2024-09-17 DOI:arxiv-2409.10817

Masato Hoshino

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引用次数: 0

摘要

博尼准积是准控制微积分理论的主要工具之一。旁积通常是通过傅立叶分析定义的，因此它不是一个局部算子。然而，在之前的研究[7, 8]中，作者证明了当正则之和小于 1 时，对于旁积及其iterated 版本，类似 (1.2) 的点估计是成立的。

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A note on the Taylor estimates of iterated paraproducts

Bony's paraproduct is one of the main tools in the theory of paracontrolled calculus. The paraproduct is usually defined via Fourier analysis, so it is not a local operator. In the previous researches [7, 8], however, the author proved that the pointwise estimate like (1.2) holds for the paraproduct and its iterated versions when the sum of the regularities is smaller than 1. The aim of this article is to extend these results for higher regularities.

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arXiv - MATH - Probability

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