Weighted Hardy spaces associated with elliptic operators. Part II : characterizations of h1 L (w)
Martell, José María (Instituto de Ciencias Matemáticas (Madrid, Espanya))
Prisuelos-Arribas, Cruz (Instituto de Ciencias Matemáticas (Madrid, Espanya))

Date:	2018
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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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Hardy spaces ; Second order divergence form elliptic operators ; Heat and poisson semigroups ; Conical square functions ; Non-tangential maximal functions ; Molecular decomposition ; Muckenhoupt weights ; Off-diagonal estimates
Published in:	Publicacions matemàtiques, Vol. 62 Núm. 2 (2018) , p. 475-535 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/338220
DOI: 10.5565/PUBLMAT6221806

61 p, 718.5 KB

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