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The Cauchy integral, bounded and compact commutators (1709.00703v2)
Published 3 Sep 2017 in math.CA
Abstract: We study the commutator of the well-known Cauchy integral operator with a locally integrable function $b$ on $\mathbb R$, and establish the characterisation of the BMO space on $\mathbb R$ via the $Lp$ boundedness of this commutator. Moreover, we also establish the characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator.