Weighted hardy spaces associated with elliptic operators. Part II: Characterizations of HL 1(w)
Given a Muckenhoupt weight w and a second order divergence form elliptic operator L, we consider different versions of the weighted Hardy space H (w) defined by conical square functions and non-tangential maximal functions associated with the heat and Poisson semigroups generated by L. We show that...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/190469 |
| Acceso en línea: | http://hdl.handle.net/10261/190469 |
| Access Level: | acceso abierto |
| Palabra clave: | Muckenhoupt weights molecular decomposition Conical square functions Hardy spaces second order divergence form elliptic operators Heat and Poisson semigroups o-diagonal estimates non-tangential maximal functions |
| Sumario: | Given a Muckenhoupt weight w and a second order divergence form elliptic operator L, we consider different versions of the weighted Hardy space H (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 H (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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