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arXiv · 1903.06208

Weighted estimates for maximal functions associated to skeletons

Andrea Olivo·Ezequiel Rela
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Abstract

We provide quantitative weighted estimates for the $L^p(w)$ norm of a maximal operator associated to cube skeletons in $\mathbb{R}^n$. The method of proof differs from the usual in the area of weighted inequalities since there are no covering arguments suitable for the geometry of skeletons. We use instead a combinatorial strategy that allows to obtain, after a linearization and discretization, $L^p$ bounds for the maximal operator from an estimate related to intersections between skeletons and $k$-planes.

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Andrea Olivo, Ezequiel Rela. 2019-03-14. Weighted estimates for maximal functions associated to skeletons. https://arxiv.org/abs/1903.06208

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