PreprintarXiv licencearXiv
The square function estimate for the cone in four dimensions
Abstract
We obtain the L3 reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a preliminaries section. The proof passes from geometric concentration of packet coefficients to regularity of the analyzed wave, and then from free waves to arbitrary functions supported near the cone. As a consequence, we obtain the corresponding L3 estimate for the sphere and elliptic paraboloids in three dimensions.
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BibTeX
@misc{temur2026square,
title = {{The square function estimate for the cone in four dimensions}},
author = {Faruk Temur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12681},
eprint = {2610.12681},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12681},
}
RIS
TY - UNPB
TI - The square function estimate for the cone in four dimensions
AU - Faruk Temur
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12681
UR - https://arxiv.org/abs/2610.12681
AB - We obtain the L^3 reverse square function estimate for the light cone in four dimensions from the critical local-smoothing and round-cone propagation statements in the September 2026 OpenAI manuscript. We state these inputs, together with the plate maximal theorem of Di Plinio and Parissis, in a preliminaries section. The proof passes from geometric concentration of packet coefficients to regularity of the analyzed wave, and then from free waves to arbitrary functions supported near the cone. As a consequence, we obtain the corresponding L^3 estimate for the sphere and elliptic paraboloids in three dimensions.
ER -