RD 空间上 Journé 类积奇异积分算子的加权估计值

IF 1 3区 数学 Q1 MATHEMATICS Forum Mathematicum Pub Date : 2024-04-17 DOI:10.1515/forum-2023-0273
Taotao Zheng, Yanmei Xiao, Xiangxing Tao
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引用次数: 0

摘要

RD 空间 𝑀 是 Coifman 和 Weiss 意义上的均质型空间,其附加性质是反向倍增性质在 𝑀 中成立。在本文中,作者首先给出了 RD 空间上积加权 Triebel-Lizorkin 空间和积加权 Besov 空间的 Plancherel-Pôlya 特性,并对这些函数空间上 Journé 类中的积奇异积分算子做了一些估计。根据这些结论,他们提出了积 Lipschitz 空间和积加权 Hardy 空间上积奇异积分算子有界性的一些充分条件。其次,通过提升和投影算子的有界性,他们还得到了乘积加权哈代空间的对偶空间是乘积加权卡列松度量空间。利用对偶的思想,作者得到了乘积加权卡列松度量空间上奇异积分算子的加权有界性。
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Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
An RD-space 𝑀 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝑀. In this paper, firstly, the authors give the Plancherel–Pôlya characterization of product weighted Triebel–Lizorkin spaces and product weighted Besov spaces on RD-spaces and make some estimates for the product singular integral operators in Journé’s class on these function spaces. As a result of these conclusions, they present some sufficient conditions for the boundedness of product singular integral operators on the product Lipschitz spaces and product weighted Hardy spaces. Secondly, by the boundedness of lifting and projection operators, they also obtain that the dual spaces of the product weighted Hardy spaces are product weighted Carleson measure spaces. Using the idea of dual, the authors obtain the weighted boundedness of singular integral operators on the product weighted Carleson measure spaces.
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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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