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 Calder\'on--Zygmund operators on Bochner spaces and
some new local estimates.

1. Department of Mathematics
   University of Turku
   FI-20014 Turku, Finland