Journal of Geometric Analysis

, Volume 21, Issue 1, pp 118–149

The Multilinear Strong Maximal Function

Authors

    • Department of MathematicsUniversity of Missouri
  • Liguang Liu
    • Department of Mathematics, School of InformationRenmin University of China
  • Carlos Pérez
    • Departamento De Análisis Matemático, Facultad de MatemáticasUniversidad De Sevilla
  • Rodolfo H. Torres
    • Department of MathematicsUniversity of Kansas
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