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

Hytönen, Tuomas; Li, Kangwei; Oikari, Tuomas

doi:10.1090/proc/15101

Iterated commutators under a joint condition on the tuple of multiplying functions
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by Tuomas Hytönen, Kangwei Li and Tuomas Oikari PDF

Proc. Amer. Math. Soc. 148 (2020), 4797-4815 Request permission

Abstract:

We present a pair of joint conditions on the two functions $b_1,b_2$ strictly weaker than $b_1,b_2\in \operatorname {BMO}$ 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.

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