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arXiv · 0712.3114

New Abstract Hardy Spaces

Frederic Bernicot·Jiman Zhao
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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. Then we apply this abstract theory to the L^p maximal regularity. Finally we present partial results in order to understand a characterization of the duals of Hardy spaces.

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Frederic Bernicot, Jiman Zhao. 2007-12-19. New Abstract Hardy Spaces. https://arxiv.org/abs/0712.3114

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