Endpoint eigenfunction bounds for the Hermite operator

  • Eunhee Jeong

    Jeonbuk National University, Jeonju, South Korea
  • Sanghyuk Lee

    Seoul National University, Seoul, South Korea
  • Jaehyeon Ryu

    Korea Institute for Advanced Study, Seoul, South Korea
Endpoint eigenfunction bounds for the Hermite operator cover

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Abstract

We establish the optimal , , eigenfunction bound for the Hermite operator on . Let denote the projection operator to the vector space spanned by the eigenfunctions of with eigenvalue . The optimal bounds on , , have been known by the works of Karadzhov and Koch–Tataru except . For , we prove the optimal bound for the missing endpoint case. Our result is built on a new phenomenon: improvement of the bound due to asymmetric localization near the sphere .

Cite this article

Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu, Endpoint eigenfunction bounds for the Hermite operator. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1495