New Abstract Hardy Spaces
Functional Analysis
2007-12-20 v1 Analysis of PDEs
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.
Cite
@article{arxiv.0712.3114,
title = {New Abstract Hardy Spaces},
author = {Frederic Bernicot and Jiman Zhao},
journal= {arXiv preprint arXiv:0712.3114},
year = {2007}
}
Comments
53 pages