Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type
Classical Analysis and ODEs
2025-06-09 v1 Functional Analysis
Probability
Abstract
A Mizohata-Takeuchi type estimate is a type of weighted Fourier restriction estimate. Using tools from high dimensional probability, we construct a large class of weights that satisfy sharp estimates of Mizohata-Takeuchi type. One can interpret our result as saying that with high probability, a generic weight satisfies a sharp inequality of Mizohata-Takeuchi type (up to an epsilon-loss).
Cite
@article{arxiv.2506.05624,
title = {Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type},
author = {Siddharth Mulherkar},
journal= {arXiv preprint arXiv:2506.05624},
year = {2025}
}
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