New Abstract Hardy Spaces

By Frédéric Bernicot, Jiman Zhao. 2007

65 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2722ca5130143052e01c72aa9d081e7db3189af9

How researchers see this paper

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In Applied Mathematics

1. Liang Song
2. Lixin Yan
3. Dachun Yang
4. Xuan Thinh Duong
5. Renjin Jiang
6. Sibei Yang
7. Yuan Zhou
8. S. Hofmann

In Mathematical Physics

1. Liang Song
2. Lixin Yan
3. Dachun Yang
4. Xuan Thinh Duong
5. Renjin Jiang
6. Sibei Yang
7. Yuan Zhou
8. Ji Li

Citations in the corpus

• A MAXIMAL FUNCTION CHARACTERIZATION FOR HARDY SPACES ASSOCIATED TO NONNEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES (2015, background): “This topic has attracte d lot of attention in the last decades, and has been a very active research topic in harmoni c analysis – see for example, [2, 3, 4, 10, 12, 13, 16, 17, 18, 19, 25].”