Journal of Geometric Analysis

, Volume 21, Issue 1, pp 118–149

The Multilinear Strong Maximal Function

  • Loukas Grafakos
  • Liguang Liu
  • Carlos Pérez
  • Rodolfo H. Torres
Article

DOI: 10.1007/s12220-010-9174-8

Cite this article as:
Grafakos, L., Liu, L., Pérez, C. et al. J Geom Anal (2011) 21: 118. doi:10.1007/s12220-010-9174-8

Abstract

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Bilinear interpolation results between distributional estimates, such as those satisfied by the multivariable strong maximal function, are also proved.

Keywords

Maximal operatorsWeighted norm inequalitiesMultilinear singular integralsCalderón–Zygmund theoryCommutators

Mathematics Subject Classification (2000)

42B2042B2546B7047B38

Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  • Loukas Grafakos
    • 1
  • Liguang Liu
    • 2
  • Carlos Pérez
    • 3
  • Rodolfo H. Torres
    • 4
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of Mathematics, School of InformationRenmin University of ChinaBeijingChina
  3. 3.Departamento De Análisis Matemático, Facultad de MatemáticasUniversidad De SevillaSevillaSpain
  4. 4.Department of MathematicsUniversity of KansasLawrenceUSA