Two Weight Inequalities for Iterated Commutators with Calderón-Zygmund Operators

2015/09/12 by Irina Holmes, Holmes, Irina, Brett D. Wick +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1509.03769

openalex publication_date 2015/09/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Given a Calderón-Zygmund operator T, a classic result of Coifman-Rochberg-Weiss relates the norm of the commutator [b, T] with the BMO norm of b. We focus on a weighted version of this result, obtained by Bloom and later generalized by Lacey and the authors, which relates ‖ [b, T] : L^p(ℝⁿ; μ) → L^p(ℝⁿ; λ) ‖ to the norm of b in a certain weighted BMO space determined by A_p weights μ and λ. We extend this result to higher iterates of the commutator and recover a one-weight result of Chung-Pereyra-Perez in the process.

Related

• New oscillation classes and two weight bump conditions for commutators
• Upper Bound for Multi-parameter Iterated Commutators
• On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
• Calderón-Zygmund operators and commutators in spaces of homogeneous type: weighted inequalities
• Some estimates for commutators of Calderón-Zygmund operators on the weighted Morrey spaces