Dyadic bi-parameter simple commutator and dyadic little BMO

2020/12/10 by Irina Holmes, Sergei Treil, Holmes, Irina +3
Mathematics · #42B100 #42B35 #47A100 #Advanced Algebra and Geometry #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2012.05376

openalex publication_date 2020/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \bfT is a certain tensor product of simple dyadic shifts defined below. We prove here that for dyadic bi-parameter commutator the following equivalence holds ‖\bfT b-b \bfT ‖ \asymp ‖b‖_bmo^d. This result is well-known for many types of bi-parameter commutators, see \citeFS, \citeDLWY and \citeDPSK for more details.

Related

• Dyadic bi-parameter repeated commutator and dyadic product BMO
• Dyadic lower little BMO estimates
• Optimal Sparse Bounds and Commutator Characterizations Without Doubling
• Dyadic product BMO in the Bloom setting
• Characterization of two parameter matrix-valued BMO by commutator with the Hilbert transform