Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces

IF 1 3区 数学 Q1 MATHEMATICS Forum Mathematicum Pub Date : 2024-08-05 DOI:10.1515/forum-2023-0454
Jiawei Tan, Qingying Xue
{"title":"Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces","authors":"Jiawei Tan, Qingying Xue","doi":"10.1515/forum-2023-0454","DOIUrl":null,"url":null,"abstract":"In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calderón–Zygmund operators.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"12 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Forum Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/forum-2023-0454","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calderón–Zygmund operators.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
函数空间多线性伪微分算子的定量加权估计
本文在重排不变的巴拿赫和准巴拿赫空间中系统地研究了多线性伪微分算子的加权估计。这些空间的典型例子包括 Lebesgue 空间、经典洛伦兹空间和 Marcinkiewicz 空间。更确切地说,我们为多线性伪微分算子及其换元建立了加权有界性和加权模态估计,包括弱端点情况。作为应用,我们证明了上述结果也适用于多线性傅里叶乘数、多线性平方函数和一类多线性卡尔德龙-齐格蒙算子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Forum Mathematicum
Forum Mathematicum 数学-数学
CiteScore
1.60
自引率
0.00%
发文量
78
审稿时长
6-12 weeks
期刊介绍: Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.
期刊最新文献
Is addition definable from multiplication and successor? The stable category of monomorphisms between (Gorenstein) projective modules with applications Big pure projective modules over commutative noetherian rings: Comparison with the completion Discrete Ω-results for the Riemann zeta function Any Sasakian structure is approximated by embeddings into spheres
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1