Abstract
The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H 1 . We construct spaces through an atomic (or molecular) decomposition. We prove some results about continuity from these spaces into L 1 and some results about interpolation between these spaces and the Lebesgue spaces. We also obtain some results on weighted norm inequalities. Finally we present partial results in order to understand a characterization of the duals of Hardy spaces.
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