Weighted L² estimates with applications to L^p problems

2025/06/03 by Wu, Shukun
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.02650

Abstract

We establish some weighted L² estimates for the Fourier extension operator in ℝ² and discuss several applications to L^p problems. These include estimates for the maximal Schrödinger operator and the maximal extension operator, decay of circular L^p-means of Fourier transform of fractal measures, and an L^p analogue of the Mizohata-Takeuchi conjecture.

Citations

• Large value estimates in number theory, harmonic analysis, and computer science
• Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities
• On almost everywhere convergence of planar Bochner-Riesz means
• On Falconer's distance set problem in the plane
• The proof of the l² Decoupling Conjecture
• A restriction estimate using polynomial partitioning

Related

• L^p weighted Fourier restriction estimates
• L^p estimates of the maximal Schrödinger operator in \mathbb Rⁿ
• Mizohata-Takeuchi inequalities for orthonormal systems
• A solution of an L² extension problem with optimal estimate and applications
• On L^p extremals for Fourier extension estimate to fractional surface