Schatten classes and commutator in the two weight setting, I. Hilbert transform

2022/02/24 by Lacey, Michael, Li, Ji, Wick, Brett D.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2202.11854

Abstract

We characterize the Hilbert--Schmidt class membership of commutator with the Hilbert transform in the two weight setting. The characterization depends upon the symbol of the commutator being in a new weighted Besov space. This follows from a Schatten class S_p result for dyadic paraproducts, where 1< p < ∞ . We discuss the difficulties in extending the dyadic result to the full range of Schatten classes for the Hilbert transform.

Related

• Schatten classes and commutators in the two weight setting, II. Riesz transforms
• Besov Space, Schatten Classes And Commutators Of Riesz Transforms Associated With The Neumann Laplacian
• Besov Spaces, Schatten Classes and Weighted Versions of the Quantised Derivative
• Complex median method and Schatten class membership of commutators
• Schatten p class commutators on the weighted Bergman space L²_a (\mathbbB_n, dv_γ) for (2n)/(n + 1 + γ) < p < ∞