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arXiv · 1604.06791

On the harmonic and geometric maximal operators

Linden Anne Duffee·Kabe Moen
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Abstract

We examine the harmonic and geometric maximal operators defined for a general basis of open sets in $\R^n$. 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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Linden Anne Duffee, Kabe Moen. 2016-04-22. On the harmonic and geometric maximal operators. https://arxiv.org/abs/1604.06791

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