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New Abstract Hardy Spaces

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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Contributor : Frederic Bernicot <>
Submitted on : Saturday, January 26, 2008 - 8:08:40 PM
Last modification on : Wednesday, October 14, 2020 - 4:04:59 AM

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  • HAL Id : hal-00218335, version 1
  • ARXIV : 0712.3114



Frederic Bernicot, Jiman Zhao. New Abstract Hardy Spaces. Journal of Functional Analysis, Elsevier, 2008, 255 (7), pp.1761-1796. ⟨hal-00218335⟩



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