Maximal multilinear operators

Demeter, Ciprian; Tao, Terence; Thiele, Christoph

doi:10.1090/S0002-9947-08-04474-7

Maximal multilinear operators
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by Ciprian Demeter, Terence Tao and Christoph Thiele PDF

Trans. Amer. Math. Soc. 360 (2008), 4989-5042 Request permission

Abstract:

We establish multilinear $L^p$ bounds for a class of maximal multilinear averages of functions of one variable, reproving and generalizing the bilinear maximal function bounds of Lacey (2000). As an application we obtain almost everywhere convergence results for these averages, and in some cases we also obtain almost everywhere convergence for their ergodic counterparts on a dynamical system.

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