Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters

Shengwen Gan; Cheng Zhang; Zhifei Zhu

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arXiv · 2606.26550

Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters

Shengwen Gan·Cheng Zhang·Zhifei Zhu

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Abstract

We prove sharp $k$-linear $L^p$ estimates for Carleson--Sj\"olin oscillatory integral operators with arbitrary separated frequency scales for all $k\ge 2$ and $1\le p\le \infty$. The estimates are sharp, including the endpoint logarithmic behavior for general Carleson--Sj\"olin phases. Moreover, we obtain log-free endpoint bilinear spectral cluster estimates on every closed three-dimensional Riemannian manifold, resolving a problem of Burq--G\'erard--Tzvetkov. As a consequence, we establish sharp $k$-linear $L^p$ spectral cluster estimates for all $k\ge 2$ and $1\le p\le \infty$.

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BibTeX RIS

Shengwen Gan, Cheng Zhang, Zhifei Zhu. 2026-06-25. Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters. https://arxiv.org/abs/2606.26550

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