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Endpoint maximal estimates for the half-wave propagator
Abstract
We present a proof of the strong maximal estimate for the Euclidean half-wave propagator at the critical pair sd=d/(d+1) and qd=2(d+1)/(d−1), in every dimension d≥2, i.e. biggl|sup0<t<1|eit√(−Δ)f(x)|biggl|Lqd(ℝd) ≤ Cd|f| Hsd(ℝd).
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BibTeX
@misc{an2026endpoint,
title = {{Endpoint maximal estimates for the half-wave propagator}},
author = {Bowen An and Wenjuan Li and Huiju Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27004},
eprint = {2610.27004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27004},
}
RIS
TY - UNPB
TI - Endpoint maximal estimates for the half-wave propagator
AU - Bowen An
AU - Wenjuan Li
AU - Huiju Wang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27004
UR - https://arxiv.org/abs/2610.27004
AB - We present a proof of the strong maximal estimate for the Euclidean half-wave propagator at the critical pair s_d=d/(d+1) and q_d=2(d+1)/(d−1), in every dimension d≥2, i.e. biggl|sup_0<t<1|e^it√(−Δ)f(x)|biggl|_L^q_d(ℝ^d) ≤ C_d|f|_ H^s_d(ℝ^d).
ER -