Article
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
Author/s | Lerner, Andrei K.
Ombrosi, Sheldy J. Pérez Moreno, Carlos Torres, Rodolfo H. Trujillo González, Rodrigo Francisco |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2009-03-01 |
Deposit Date | 2016-10-10 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España National Science Foundation (NSF). United States |
Project ID. | MTM2006-05622
![]() MTM2005-07347 ![]() OISE 0126272 ![]() DMS 0400423 ![]() |
Citation | Lerner, A.K., Ombrosi, S.J., Pérez Moreno, C., Torres, R.H. y Trujillo González, R.F. (2009). New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory. Advances in Mathematics, 220 (4), 1222-1264. |
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