On the harmonic and geometric maximal operators

2016/04/22 by Duffee, Linden Anne, Moen, Kabe
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.06791

Abstract

We examine the harmonic and geometric maximal operators defined for a general basis of open sets in \Rⁿ. We prove two weight norm inequalities for the harmonic maximal operator assuming testing conditions over characteristic functions of unions of sets from the basis. We also prove a that a bumped two weight A_p-like condition is sufficient for the two weight boundedness of the harmonic maximal operator.

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