Iterated commutators under a joint condition on the tuple of multiplying functions

Abstract

We present a pair of joint conditions on the two functions $b_1,b_2$ strictly weaker than $b_1,b_2\in \mathrm{BMO}$ that almost characterize the $L^2$ boundedness of the iterated commutator $[b_2,[b_1,T]]$ of these functions and a Calderón-Zygmund operator $T.$ Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.

14 pages, article restructured for improved presentation in accordance with referee comments

References in corpus (2)

• On pointwise estimates involving sparse operators
• Commutators of singular integrals revisited