Weighted Hardy spaces associated with elliptic operators. Part IIcharacterizations of h1 L (w)

  1. José María Martell
  2. María Cruz Prisuelos Arribas
Journal:
Publicacions matematiques

ISSN: 0214-1493

Year of publication: 2018

Volume: 62

Issue: 2

Pages: 475-535

Type: Article

DOI: 10.5565/PUBLMAT6221806 DIALNET GOOGLE SCHOLAR lock_openDDD editor

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Abstract

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.

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Funding information

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.

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