{"title":"A note on the Taylor estimates of iterated paraproducts","authors":"Masato Hoshino","doi":"arxiv-2409.10817","DOIUrl":null,"url":null,"abstract":"Bony's paraproduct is one of the main tools in the theory of paracontrolled\ncalculus. The paraproduct is usually defined via Fourier analysis, so it is not\na local operator. In the previous researches [7, 8], however, the author proved\nthat the pointwise estimate like (1.2) holds for the paraproduct and its\niterated versions when the sum of the regularities is smaller than 1. The aim\nof this article is to extend these results for higher regularities.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10817","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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