A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator
Volume 253 / 2020
Studia Mathematica 253 (2020), 307-327
MSC: Primary 42B35; Secondary 42B25.
DOI: 10.4064/sm190209-12-8
Published online: 6 March 2020
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 $\Gamma =\{x+iA(x): x\in \mathbb {R}\}$.
