New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to bu...
| Autores: | , , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47293 |
| Acesso em linha: | http://hdl.handle.net/11441/47293 https://doi.org/10.1016/j.aim.2008.10.014 |
| Access Level: | acceso abierto |
| Palavra-chave: | Multilinear singular integrals Calderón-Zygmund theory Maximal operators Weighted norm inequalities Commutators |
| Resumo: | A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller that the m-fold product of the Hardy-Littlewood maximal function is studied. The operator is used to obtain a precise control on multilinear singular integral operators of Calderón-Zygmund type and to build a theory of weights adapted to the multilinear setting. A natural variant of the operator which is useful to control certain commutators of multilinear Calder´on-Zygmund operators with BMO functions is then considered. The optimal range of strong type estimates, a sharp end-point estimate, and weighted norm inequalities involving both the classical Muckenhoupt weights and the new multilinear ones are also obtained for the commutators. |
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