Dyadic lower little BMO estimates

TL;DR

This paper characterizes dyadic little BMO spaces through the boundedness of tensor commutators with dyadic shifts, extending the understanding of these function spaces in both weighted and unweighted contexts.

Contribution

It introduces a novel characterization of dyadic little BMO using tensor commutators and explores multiple proof strategies, including their adaptability to Bloom weights.

Findings

Dyadic little BMO characterized via tensor commutator boundedness

Multiple proof strategies applicable in unweighted and weighted cases

Enhanced understanding of the flexibility of proof methods

Abstract

We characterize dyadic little BMO via the boundedness of the tensor commutator with a single well chosen dyadic shift. It is shown that several proof strategies work for this problem, both in the unweighted case as well as with Bloom weights. Moreover, we address the flexibility of one of our methods.