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arXiv · 1709.00703

The Cauchy integral, bounded and compact commutators

Ji Li·Trang T. T. Nguyen·Lesley A. Ward·Brett D. Wick
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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 $L^p$ boundedness of this commutator. Moreover, we also establish the characterisation of the VMO space on $\mathbb R$ via the compactness of this commutator.

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Ji Li, Trang T. T. Nguyen, Lesley A. Ward, Brett D. Wick. 2020-02-19. The Cauchy integral, bounded and compact commutators. https://doi.org/10.4064/sm180715-13-12

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