Almost-orthogonal Strichartz estimates and radial improvements
Abstract
We extend the Schatten-duality principle from orthonormal systems to (almost-orthogonal) Bessel families and apply it to prove sharp and improved Bessel-family Strichartz estimates for the Kadomtsev--Petviashvili, Zakharov--Kuznetsov, and radial Schrödinger equations. In particular, for the Schrödinger equation, we establish an improved estimate in a larger radial range of space-time exponents, not from dispersive estimates as in the KP/ZK models, but from direct robust Schatten estimates, using some vector-valued multi-product trace formula and multilinear weighted fractional integral formula. To the best of our knowledge, this is the first radial improvement for systems, and the almost-orthogonal estimates are also new to the literature. We also derive necessary conditions.
Related
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BibTeX
@misc{ji2026almostorthogonal,
title = {{Almost-orthogonal Strichartz estimates and radial improvements}},
author = {Hongzhou Ji and Liping Xu and An Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30726},
eprint = {2609.30726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30726},
}
RIS
TY - UNPB
TI - Almost-orthogonal Strichartz estimates and radial improvements
AU - Hongzhou Ji
AU - Liping Xu
AU - An Zhang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30726
UR - https://arxiv.org/abs/2609.30726
AB - We extend the Schatten-duality principle from orthonormal systems to (almost-orthogonal) Bessel families and apply it to prove sharp and improved Bessel-family Strichartz estimates for the Kadomtsev--Petviashvili, Zakharov--Kuznetsov, and radial Schrödinger equations. In particular, for the Schrödinger equation, we establish an improved estimate in a larger radial range of space-time exponents, not from dispersive estimates as in the KP/ZK models, but from direct robust Schatten estimates, using some vector-valued multi-product trace formula and multilinear weighted fractional integral formula. To the best of our knowledge, this is the first radial improvement for systems, and the almost-orthogonal estimates are also new to the literature. We also derive necessary conditions.
ER -