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A sharpened L8t L4x-Strichartz estimate for even initial data
Abstract
It is well known that u0 ∈ L2(ℝ) ∖ {0} is an extremizer for the L8t L4x-Strichartz estimate if and only if it is a Gaussian. We show that every extremizing sequence of even functions { un } ⊂ L2(ℝ) ∖ {0} approaches a centered Gaussian in an appropriate sense. This result follows from a certain inequality for coordinate-wise even L2 functions on ℝ4 conjectured by Gonçalves (2019) which we prove in this paper with the optimal constant.
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BibTeX
@misc{suzuki2026sharpened,
title = {{A sharpened $L^8_t L^4_x$-Strichartz estimate for even initial data}},
author = {Soichiro Suzuki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31543},
eprint = {2610.31543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31543},
}
RIS
TY - UNPB
TI - A sharpened L^8_t L^4_x-Strichartz estimate for even initial data
AU - Soichiro Suzuki
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31543
UR - https://arxiv.org/abs/2610.31543
AB - It is well known that u_0 ∈ L^2(ℝ) ∖ {0} is an extremizer for the L^8_t L^4_x-Strichartz estimate if and only if it is a Gaussian. We show that every extremizing sequence of even functions { u_n } ⊂ L^2(ℝ) ∖ {0} approaches a centered Gaussian in an appropriate sense. This result follows from a certain inequality for coordinate-wise even L^2 functions on ℝ^4 conjectured by Gonçalves (2019) which we prove in this paper with the optimal constant.
ER -