Sharp ℓ^q(L^p) decoupling for paraboloids

2024/04/27 by Tongou Yang, Yang, Tongou
Mathematics · #Mathematical Approximation and Integration #Numerical methods in inverse problems #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2404.17748

Abstract

In this short expository note, we prove the following result, which is a special case of the main theorem in arXiv:2011.09451. For each n ≥ 2 and p, q ∈ [2, ∞], we prove upper bounds of ℓ^q(L^p) decoupling constants for paraboloids in \mathbb Rⁿ, as well as presenting extremisers for each case. Both are sharp up to ε-losses.

Related

• On decoupling and restriction estimates
• A study guide for the ℓ² decoupling theorem for the paraboloid
• Small cap decoupling for the paraboloid in ℝⁿ
• An introduction to decoupling and harmonic analysis over ℚ_p
• Mixed norm l² decoupling for paraboloids