The multilinear strong maximal function
Classical Analysis and ODEs
2011-03-10 v2 Functional Analysis
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. Certain bilinear interpolation results between distributional estimates, such as that obtained for the multivariable strong maximal function, are also proved.
Cite
@article{arxiv.1002.1412,
title = {The multilinear strong maximal function},
author = {Loukas Grafakos and Liguang Liu and Carlos Perez and Rodolfo H. Torres},
journal= {arXiv preprint arXiv:1002.1412},
year = {2011}
}
Comments
appeared in J. of Geometric Anal