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Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type (2506.05624v1)
Published 5 Jun 2025 in math.CA, math.FA, and math.PR
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).