Schatten classes and commutators in the two weight setting, II. Riesz transforms

2024/03/30 by Michael T. Lacey, Ji Li, Lacey, Michael +5
Mathematics · #Advanced Operator Algebra Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.00329

openalex publication_date 2024/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the Schatten class S^p of the commutator of Riesz transforms [b,R_j] in \mathbb Rⁿ (j=1,…, n) in the two weight setting for n< p<∞, by introducing the condition that the symbol b being in Besov spaces associated with the given two weights. At the critical index p=n, the commutator [b,R_j] belongs to Schatten class Sⁿ if and only if b is a constant, and to the weak Schatten class S^n,∞ if and only if b is in an oscillation sequence space associated with the given two weights. As a direct application, we have the Schatten class estimate for A. Connes' quantised derivative in the two weight setting.

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