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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal multilinear operators


Authors: Ciprian Demeter, Terence Tao and Christoph Thiele
Journal: Trans. Amer. Math. Soc. 360 (2008), 4989-5042
MSC (2000): Primary 42B25; Secondary 37A45
Published electronically: April 21, 2008
MathSciNet review: 2403711
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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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Additional Information

Ciprian Demeter
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
Email: demeter@math.ucla.edu

Terence Tao
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
Email: tao@math.ucla.edu

Christoph Thiele
Affiliation: Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
Email: thiele@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04474-7
PII: S 0002-9947(08)04474-7
Keywords: Maximal operators, multilinear averages
Received by editor(s): November 30, 2005
Received by editor(s) in revised form: October 27, 2006
Published electronically: April 21, 2008
Additional Notes: The first author was supported by NSF Grant DMS-0556389
The second author was supported by NSF Grant CCF-0649473 and a grant from the McArthur Foundation
The third author was supported by NSF Grants DMS-0400879 and DMS-0701302
Article copyright: © Copyright 2008 American Mathematical Society