A trilinear approach to square function and local smoothing estimates\n for the wave operator

2016/07/28 by Jungjin Lee, Lee, Jungjin · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1607.08426

openalex publication_date 2016/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to improve the known estimates for Mockenhaupt's\nsquare function in mathbb R³ and for Sogge's local smoothing in mathbb\nR²⁺¹ spacetime. For this we use the trilinear approach of S. Lee and A.\nVargas for the cone multiplier with some trilinear estimates obtained from the\n\ℓ² decoupling theorem and multilinear restriction theorem.\n

Citations

• Estimates for translation invariant operators in Lp spaces
• On the multilinear restriction and Kakeya conjectures

Cited by

• Local smoothing and maximal estimates for average over surfaces of codimension 2 in \mathbb R⁴

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