卡尔德龙-齐格蒙德算子的沙腾类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-10 DOI:10.1007/s00041-023-10059-7

Paco Villarroya

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引用次数: 0

摘要

我们证明了卡尔德龙-齐格蒙算子属于沙腾类的充分条件。与经典的 T1 理论一样，这些条件是根据算子核的平滑性以及算子及其对函数 1 的作用给出的。为了证明当 \(p>2\)时属于沙腾类，我们为组成的卡尔德龙-齐格蒙德算子开发了新的碰撞估计，并对卡列森嵌入定理进行了新的扩展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Schatten Classes of Calderón–Zygmund Operators

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The Schatten Classes of Calderón–Zygmund Operators

We prove sufficient conditions for a Calderón–Zygmund operator to belong to the Schatten classes. As in the classical T1 theory, the conditions are given in terms of the smoothness of the operator kernel, and the action of both the operator and its adjoint on the function 1. To show membership to the Schatten class when \(p>2\) we develop new bump estimates for composed Calderón–Zygmund operators, and a new extension of Carleson’s Embedding Theorem.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.