Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators

• Autores: Pradolini, Gladis Guadalupe
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Multilineal Operators; Fractional Integrals; Maximal Operators; Weighted Norm Inequalities
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this article we prove weighted norm inequalities and pointwise estimates between the multilinear fractional integral operator and the multilinear fractional maximal. As a consequence of these estimations we obtain weighted weak and strong inequalities for the multilinear fractional maximal operator or function. In particular, we extend some results given in Carro et al. (2005) [7] to the multilinear context. On the other hand we prove weighted pointwise estimates between the multilinear fractional maximal operator Mα, B associated to a Young function B and the multilinear maximal operators Mψ = M0, ψ, ψ (t) = B (t1 - α / (n m))n m / (n m - α). As an application of these estimate we obtain a direct proof of the Lp - Lq boundedness results of Mα, B for the case B (t) = t and Bk (t) = t (1 + log+ t)k when 1 / q = 1 / p - α / n. We also give sufficient conditions on the weights involved in the boundedness results of Mα, B that generalizes those given in Moen (2009) [22] for B (t) = t. Finally, we prove some boundedness results in Banach function spaces for a generalized version of the multilinear fractional maximal operator.
Fil: Pradolini, Gladis Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina