Weighted mixed weak-type inequalities for multilinear operators
In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x)...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/86012 |
| Acceso en línea: | http://hdl.handle.net/11336/86012 |
| Access Level: | acceso abierto |
| Palabra clave: | MULTILINEAR OPERATORS MIXED WEIGHTED INEQUALITIES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we present a theorem that generalizes Sawyer’s classic result about mixed weighted inequalities to the multilinear context. Let ~w = (w1, ..., wm) and ν = w 1 m 1 ...w 1 mm , the main result of the paper sentences that under different conditions on the weights we can obtain T ( ~f )(x) v L 1m ,∞(νv 1m ) ≤ C Ym i=1 kfikL1(wi), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for M(f~)(x): the multi(sub)linear maximal function introduced in [13]. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators. |
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