The Cauchy integral, bounded and compact commutators
Volume 250 / 2020
Studia Mathematica 250 (2020), 193-216
MSC: Primary 42B35; Secondary 42B20.
DOI: 10.4064/sm180715-13-12
Published online: 29 July 2019
Abstract
We study the commutator of the well-known Cauchy integral with a locally integrable function $b$ on $\mathbb R$, and establish a characterisation of the BMO space on $\mathbb R$ via the $L^p$ boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator.
