Weighted Hardy spaces associated with elliptic operators. Part IIcharacterizations of h1 L (w)
- José María Martell
- María Cruz Prisuelos Arribas
ISSN: 0214-1493
Année de publication: 2018
Volumen: 62
Número: 2
Pages: 475-535
Type: Article
D'autres publications dans: Publicacions matematiques
Objectifs de Développement Durable
Résumé
Given a Muckenhoupt weight w and a second order divergence form elliptic operator L, we consider different versions of the weighted Hardy space H1 L (w)defined by conical square functions and non-tangential maximal functions associated with the heat and Poisson semigroups generated by L. We show that all of them are isomorphic and also that H1 L (w) admits a molecular characterization. One of the advantages of our methods is that our assumptions extend naturally the unweighted theory developed by S. Hofmann and S. Mayboroda in [19] and we can immediately recover the unweighted case. Some of our tools consist in establishing weighted norm inequalities for the non-tangential maximal functions, as well as comparing them with some conical square functions in weighted Lebesgue spaces.
Information sur le financement
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC agreement no. 615112 HAPDEGMT. Both authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554). Both authors would like to thank P. Auscher for his useful comments and suggestions.Financeurs
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Seventh Framework Programme
European Union
- 615112
- European Research Council European Union
- Seventh Framework Programme European Union