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Maximal transference and summability of multilinear Fourier series

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

Loukas Grafakos  and
Petr Honzík
Loukas Grafakos
Affiliation:
Department of Mathematics, University of Missouri, Columbia MO 65211, USA, e-mail: loukas@math.missouri.edu
Petr Honzík
Affiliation:
Department of Mathematics, Michigan State University, East Lansing MI 48824, USA, e-mail: petrhonz@math.msu.edu
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Abstract

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We obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m–linear Fourier series. We formulate conditions for the convergence of multilinear series and we investigate certain kinds of summation.

MSC classification

Secondary: 42B15: Multipliers 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 1 , February 2006 , pp. 65 - 80
Copyright
Copyright © Australian Mathematical Society 2006

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