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 than 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...
| Authors: | , , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2009 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/79548 |
| Online Access: | http://hdl.handle.net/11336/79548 |
| Access Level: | Open access |
| Keyword: | CalderÓN-Zygmund Theory Commutators Maximal Operators Multilinear Singular Integrals Weighted Norm Inequalities https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | A multi(sub)linear maximal operator that acts on the product of m Lebesgue spaces and is smaller than 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 Calderón-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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