Vanishing moments for scaling vectors.
Vector-valued wavelets and the Hardy space H¹(ℝⁿ,X)
We prove an analogue of Y. Meyer's wavelet characterization of the Hardy space H¹(ℝⁿ) for the space H¹(ℝⁿ,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.