振荡积分算子的双线性稀疏支配

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-04 DOI:10.1007/s13324-024-00895-1

Tobias Mattsson

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引用次数: 0

摘要

在本文中，我们证明了一般秩的一大类傅里叶积分算子的双线性稀疏支配边界，以及与所有 \(0\le \rho \le 1\) 和 \(0\le \delta < 1\) 的赫尔曼德符号类 \(S^m_\{rho ,\delta }\) 相关的振荡积分算子，薛定谔算子就是一个显著的例子。因此，我们可以得到这些类算子的弱（1，1）估计值、向量值估计值和各种加权规范不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Bilinear sparse domination for oscillatory integral operators

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Bilinear sparse domination for oscillatory integral operators

In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to Hörmander symbol classes \(S^m_{\rho ,\delta }\) for all \(0\le \rho \le 1\) and \(0\le \delta < 1\), a notable example is the Schrödinger operator. As a consequence, one obtains weak (1, 1) estimates, vector-valued estimates, and a wide range of weighted norm inequalities for these classes of operators.

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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.