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Critical orthonormal Strichartz estimates for Lebesgue spaces
Abstract
We study orthonormal Strichartz estimates at the critical coefficient exponent q/2 for fractional Schrödinger propagators. The proof for d≥3 combines annular Schatten estimates with a frequency summation argument based on potential duality and Littlewood--Paley theory. In dimension two, a trace computation supplies the annular estimate needed for the global estimate. We also construct a counterexample to the global estimate with spatial L∞ and coefficients in ℓq/2, even with a weak time norm.
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BibTeX
@misc{gong2026critical,
title = {{Critical orthonormal Strichartz estimates for Lebesgue spaces}},
author = {Yinghao Gong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03527},
eprint = {2611.03527},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03527},
}
RIS
TY - UNPB
TI - Critical orthonormal Strichartz estimates for Lebesgue spaces
AU - Yinghao Gong
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03527
UR - https://arxiv.org/abs/2611.03527
AB - We study orthonormal Strichartz estimates at the critical coefficient exponent q/2 for fractional Schrödinger propagators. The proof for d≥3 combines annular Schatten estimates with a frequency summation argument based on potential duality and Littlewood--Paley theory. In dimension two, a trace computation supplies the annular estimate needed for the global estimate. We also construct a counterexample to the global estimate with spatial L^∞ and coefficients in ℓ^q/2, even with a weak time norm.
ER -