Maximal estimates of the Schrödinger operators with quadratic potential for orthonormal systems
Abstract
We establish an equivalence principle for local mixed-norm estimates for generalized Schrödinger propagators acting on orthonormal systems. Under suitable mixed-norm conditions, estimates for generalized propagators follow from the corresponding free Schrödinger estimates for every summability exponent 1≤β≤2. Applications include maximal estimates for Schrödinger equations with time-dependent quadratic potentials and for the special Hermite operator, as well as almost everywhere convergence of the associated densities. For the special Hermite operator, we also obtain a single-function maximal estimate that is sharp up to the endpoint. We construct counterexamples for the Schrödinger operator, by combining single particle and many particle constructions in complementary dimensions, yielding new necessary conditions in an intermediate range of summability exponents.
Related
- Orthonormal maximal estimates for fractional Schrödinger operators along Hölder curves
- Orthonormal Strichartz estimates for the Schrödinger equations with Hamiltonian on Wiener amalgam spaces
- Bilinear Strichartz Estimates and Linear Morawetz Estimates for Schrödinger Operators with Potentials
- Local Smoothing Estimates of Schrödinger Operators on Waveguides Using Refined Decoupling
- Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
BibTeX
@misc{jeong2026maximal,
title = {{Maximal estimates of the Schrödinger operators with quadratic potential for orthonormal systems}},
author = {Eunhee Jeong and Hyerim Ko and Shobu Shiraki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23646},
eprint = {2610.23646},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23646},
}
RIS
TY - UNPB
TI - Maximal estimates of the Schrödinger operators with quadratic potential for orthonormal systems
AU - Eunhee Jeong
AU - Hyerim Ko
AU - Shobu Shiraki
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23646
UR - https://arxiv.org/abs/2610.23646
AB - We establish an equivalence principle for local mixed-norm estimates for generalized Schrödinger propagators acting on orthonormal systems. Under suitable mixed-norm conditions, estimates for generalized propagators follow from the corresponding free Schrödinger estimates for every summability exponent 1≤β≤2. Applications include maximal estimates for Schrödinger equations with time-dependent quadratic potentials and for the special Hermite operator, as well as almost everywhere convergence of the associated densities. For the special Hermite operator, we also obtain a single-function maximal estimate that is sharp up to the endpoint. We construct counterexamples for the Schrödinger operator, by combining single particle and many particle constructions in complementary dimensions, yielding new necessary conditions in an intermediate range of summability exponents.
ER -