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arXiv · 1902.00839

A note on weak factorization of Meyer-type Hardy space via Cauchy integral operator

Yongsheng Han·Ji Li·Cristina Pereyra·Brett D. Wick
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Abstract

This paper provides a weak factorization for the Meyer-type Hardy space $H^1_b(\mathbb{R})$, and characterizations of its dual ${\rm BMO}_b(\mathbb{R})$ and its predual ${\rm VMO}_b(\mathbb{R})$ via boundedness and compactness of a suitable commutator with the Cauchy integral $\mathscr{C}_{\Gamma}$, respectively. Here $b(x)=1+iA'(x)$ where $A'\in L^{\infty}(\mathbb{R})$, and the Cauchy integral $\mathscr{C}_{\Gamma}$ is associated to the Lipschitz curve $\Gamma=\{x+iA(x)\, : \, x\in \mathbb{R}\}$.

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Yongsheng Han, Ji Li, Cristina Pereyra, Brett D. Wick. 2019-02-03. A note on weak factorization of Meyer-type Hardy space via Cauchy integral operator. https://doi.org/10.4064/sm190209-12-8

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