Random Constructions for Sharp Estimates of Mizohata-Takeuchi Type

2025/06/05 by Siddharth Mulherkar, Mulherkar, Siddharth · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Class (philosophy) #Classical Analysis and ODEs (math.CA) #Construct (python library) #FOS: Mathematics #Fourier analysis #Fourier transform #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Inequality #Mathematical Analysis and Transform Methods #Probability (math.PR) #Type (biology)

paper · pdf · doi:10.48550/arxiv.2506.05624

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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).

Citations

• A Counterexample to the Mizohata-Takeuchi Conjecture
• On the N-set occupancy problem
• New improvement to Falconer distance set problem in higher dimensions
• Some sharp inequalities of Mizohata--Takeuchi-type
• On Falconer's distance set problem in the plane
• Duality of metric entropy
• Constructions of Majorizing Measures, Bernoulli processes and cotype

Cited by

• Power loss for the Mizohata-Takeuchi conjecture on C^k convex hypersurfaces

Related

• A weighted formulation of refined decoupling and inequalities of Mizohata-Takeuchi-type for the moment curve
• Mizohata-Takeuchi inequalities for orthonormal systems
• A Counterexample to the Mizohata-Takeuchi Conjecture
• Weighted restriction estimates and application to Falconer distance set problem
• Mizohata-Takeuchi estimates in the plane