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New abstract Hardy spaces |
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| Authors: | Fré dé ric Bernicot |
| Affiliation: | a Université Paris-Sud, Orsay et CNRS 8628, 91405 Orsay Cedex, France b School of Mathematical Sciences, Beijing Normal University, Key Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China |
| 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 H1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about continuity from these spaces into L1 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. |
| Keywords: | Hardy spaces Atomic and molecular decomposition Interpolation |
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