Oscillatory integral operators with homogeneous phase functions

Journal d'Analyse Mathématique Pub Date : 2023-12-12 DOI:10.1007/s11854-023-0320-1

引用次数: 0

Abstract

Oscillatory integral operators with 1-homogeneous phase functions satisfying a convexity condition are considered. For these we show the L^p–L^p-estimates for the Fourier extension operator of the cone due to Ou–Wang via polynomial partitioning. For this purpose, we combine the arguments of Ou–Wang with the analysis of Guth–Hickman–Iliopoulou, who previously showed sharp L^p–L^p-estimates for non-homogeneous phase functions with variable coefficients under a convexity assumption. Furthermore, we provide examples exhibiting Kakeya compression, which shows a more restrictive range than dictated by the Knapp example in higher dimensions. We apply the oscillatory integral estimates to show new local smoothing estimates for wave equations on compact Riemannian manifolds (M, g) with dim M ≥ 3. This generalizes the argument for the Euclidean wave equation due to Gao–Liu–Miao–Xi.

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具有同相函数的振荡积分算子

摘要本文考虑了具有满足凸性条件的 1 次均相函数的振荡积分算子。对于这些振荡积分算子，我们通过多项式分割，给出了欧-王（Ou-Wang）提出的锥体傅立叶扩展算子的 Lp-Lp 估计值。为此，我们将 Ou-Wang 的论点与 Guth-Hickman-Iliopoulou 的分析相结合，后者之前曾在凸性假设条件下为具有可变系数的非均相函数展示了尖锐的 Lp-Lp-estimates 。此外，我们还提供了展示 Kakeya 压缩的示例，它显示了比 Knapp 示例在更高维度上更严格的范围。我们应用振荡积分估算，为 dim M ≥ 3 的紧凑黎曼流形 (M, g) 上的波方程展示了新的局部平滑估算。这推广了高刘淼溪关于欧几里得波方程的论证。

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 d'Analyse Mathématique

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