Commutators of bilinear bi-parameter singular integrals

2018/04/17 by Kangwei Li, Li, Kangwei, Henri Martikainen +3 · 2 citations
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1804.06296

openalex publication_date 2018/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundedness properties of commutators formed by b and T, where T is a bilinear bi-parameter singular integral satisfying natural T1 type conditions and b is a little BMO function. For paraproduct free bilinear bi-parameter singular integrals T we prove that [b, T]₁ \colon L^p(ℝ^n+m) × L^q(ℝ^n+m) → L^r(ℝ^n+m) in the full range 1 < p, q ≤ ∞, 1/2 < r < ∞ satisfying 1/p+1/q = 1/r. A special case is when T is a bilinear bi-parameter multiplier. We also prove the corresponding Banach range result for all singular integrals satisfying the T1 type conditions. In doing so we simplify the corresponding linear proof. Lastly, we prove analogous results for iterated commutators.

Citations

• Banach-valued multilinear singular integrals
• Multilinear Calderón–Zygmund Theory

Cited by

• Quasi-Banach estimates of commutators of bilinear bi-parameter singular integrals: paraproducts
• Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators

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