Vector-valued wavelets and the Hardy space $H^1({\Bbb R}^n,X)$
Volume 172 / 2006
Studia Mathematica 172 (2006), 125-147
MSC: 42B30, 42C40, 46E40.
DOI: 10.4064/sm172-2-2
Abstract
We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space $H^1(\Bbb R^n)$ for the space $H^1(\Bbb R^n,X)$ of $X$-valued functions. Here $X$ is a Banach space with the UMD property. The proof uses results of T. Figiel on generalized Calderón–Zygmund operators on Bochner spaces and some new local estimates.
