New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory |
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Authors: | Andrei K. Lerner,Carlos Pé rez,Rodolfo H. Torres |
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Affiliation: | a Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080 Sevilla, Spain b Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina c Department of Mathematics, University of Kansas, 405 Snow Hall 1460 Jayhawk Blvd, Lawrence, Kansas 66045-7523, USA d Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, S.C. de Tenerife, Spain |
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Abstract: | 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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Keywords: | 42B20 42B25 |
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