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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:367

Article

Pradolini, Gladis

关键词: Multilinear operators;    Fractional integrals;    Maximal operators;    Weighted norm inequalities;   

DOI  :  10.1016/j.jmaa.2010.02.008

来源: Elsevier

【 摘 要 】

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) 17] to the multilinear context. On the other hand we prove weighted pointwise estimates between the multilinear fractional maximal operator M(alpha,beta) associated to a Young function B and the multilinear maximal operators M(psi) = M(0,psi), psi (t) = B(t(1-alpha/(nm)))(nm/(nm-alpha)). As an application of these estimate we obtain a direct proof of the L(p)-L(q) boundedness results of M(alpha,beta) for the case B(t)= t and B(k)(t) = t(1+log(+) t)(k) when 1/q = 1/p - alpha/n. We also give sufficient conditions on the weights involved in the boundedness results of M(alpha,beta) 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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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