New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory

• Autores: Andrei K. Lerner, Sheldy J. Ombrosi , Carlos Pérez Moreno , Rodolfo H. Torres, Rodrigo Trujillo González
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 220, Nº 4, 2009, págs. 1222-1264
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.10.014
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• Resumen

  • 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