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
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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.
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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。
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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.
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