Weighted Hardy spaces associated with elliptic operators. Part II: characterizations of h1 L (w)
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Autores: José María Martell Berrocal
, María Cruz Prisuelos Arribas
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 62, Nº 2, 2018, págs. 475-535
- Idioma: inglés
- DOI: 10.5565/publmat6221806
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Resumen
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.
