Journal of Fourier Analysis and Applications

, Volume 12, Issue 4, pp 447–481

Discretization and Transference of Bisublinear Maximal Operators

Article

DOI: 10.1007/s00041-006-6030-0

Cite this article as:
Berkson, E., Blasco, O., Carro, M. et al. J Fourier Anal Appl (2006) 12: 447. doi:10.1007/s00041-006-6030-0

Abstract

We develop a general condition for automatically discretizing strong type bisublinear maximal estimates that arise in the context of the real line. In particular, this method applies directly to Michael Lacey’s strong type boundedness results for the bisublinear maximal Hilbert transform and for the bisublinear Hardy-Littlewood maximal operator, furnishing the counterpart of each of these two results (without changes to the range of exponents) for the sequence spaces \(\ell^p ({\Bbb Z}).\) We then take up some transference applications of discretized maximal bisublinear operators to maximal estimates and almost everywhere convergence in Lebesgue spaces of abstract measures. We also broaden the scope of such applications, which are based on transference from \({\Bbb Z},\) by developing general methods for transplanting bisublinear maximal estimates from arbitrary locally compact abelian groups.

Copyright information

© Birkhauser Boston 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of Illinois, 1409 W. Green St.Urbana, IL 61801USA
  2. 2.Departamento de Análisis Matemático, Universidad de Valencia, 46100 (Burjassot)ValenciaSpain
  3. 3.Dept. App. Math. and Analysis, Universitat de Barcelona, Gran Via 585, 08071BarcelonaSpain
  4. 4.Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell BuildingEdinburgh EH9 3JZ, ScotlandUK

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