Compactness of commutators in the Bloom setting: the off-diagonal case
Yongming Wen
TL;DR
This paper characterizes weighted VMO spaces through the compactness of certain operators, revealing new insights even in unweighted contexts, and advances understanding of operator behavior in harmonic analysis.
Contribution
It introduces a novel characterization of weighted VMO spaces via the compactness of sparse operators and commutators, extending classical results.
Findings
Weighted VMO spaces characterized by operator compactness
New results on commutators of Riesz potentials and fractional maximal operators
Insights applicable to unweighted and weighted harmonic analysis
Abstract
In this paper, we establish a new characterization of weighted spaces, which are essential different from the classical spaces, via the compactness of sparse operators, commutators of Riesz potentials and fractional maximal operators. Some of our results are new even in unweighted setting.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Mathematical Analysis and Transform Methods