Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2509.01116

We extend the microlocal Kakeya--Nikodym bounds for eigenfunctions of Blair--Sogge to a larger range of exponents, which is optimal in odd dimensions. On manifolds of constant sectional curvature we introduce a new anisotropic variant of the microlocal Kakeya--Nikodym norm that further enlarges the admissible $p$-range. As a corollary, we obtain improved $L^p$ bounds for Hecke--Maass forms on compact hyperbolic $3$-manifolds by combining with a recent result of Hou. Further applications include sharp $L^q\!\to\!L^p$ estimates for Hörmander operators in odd dimensions, improved $L^q\!\to\!L^p$ Fourier extension bounds, and improved bounds for the Bochner--Riesz conjecture in $\mathbb R^3$.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2509.01116
PDF: https://arxiv.org/pdf/2509.01116
OA Status: green
OpenAlex ID: https://openalex.org/W4415058748

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DOI: https://doi.org/10.48550/arxiv.2509.01116

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Title: Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications

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Type: preprint

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Language: en

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Publication year: 2025

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Publication date: 2025-09-01

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Authors: Chuanwei Gao, Shukun Wu, Yakun Xi

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Landing page: https://arxiv.org/abs/2509.01116

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PDF URL: https://arxiv.org/pdf/2509.01116

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Cited by: 0

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