Sharp Fourier Extension on Fractional Surfaces

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Fourier Analysis and Applications 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

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications

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