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

Abstract

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

arXiv comment20 pages