The multilinear strong maximal function

Details The multilinear strong maximal function The multilinear strong maximal function

2010-02-06

arxiv.org/abs/1002.1412v2

J. of Geometric Anal. V. 21, (2011), 118-149

Mathematics

Classical Analysis and ODEs

appeared in J. of Geometric Anal

Scientific paper

10.1007/s12220-010-9174-8

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.

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