Sharp Fourier Extension on Fractional Surfaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-06-27 DOI:10.1007/s00041-024-10099-7

Boning Di, Dunyan Yan

引用次数: 0

Abstract

We investigate a class of Fourier extension operators on fractional surfaces \((\xi ,|\xi |^\alpha )\) with \(\alpha \ge 2\). For the corresponding \(\alpha \)-Strichartz inequalities, we characterize the precompactness of extremal sequences by applying the missing mass method and bilinear restriction theory. Our result is valid in any dimension. In particular for dimension two, our result implies the existence of extremals for \(\alpha \in [2,\alpha _0)\) with some \(\alpha _0>5\).

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分数曲面上的锐傅里叶扩展

我们研究了分数曲面 \((\xi ,|\xi |^\alpha )\) 与 \(\alpha \ge 2\) 上的一类傅里叶扩展算子。对于相应的 \(\α \)-Strichartz 不等式，我们通过应用缺失质量法和双线性限制理论来描述极值序列的预紧凑性。我们的结果在任何维度都有效。特别是对于维数二，我们的结果意味着在某些 \(\alpha _0>5\) 下 \(\alpha \in [2,\alpha _0)\)存在极值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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