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arXiv · 2407.17700

Fractional medians and their maximal functions

Yohei Tsutsui
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Abstract

In this article, we introduce the fractional medians, give an expression of the set of all fractional medians in terms of non-increasing rearrangements and then investigate mapping properties of the fractional maximal operators defined by such medians. The maximal operator is a generalization of that in Stromberg. It turns out that our maximal operator is a more smooth operator than the usual fractional maximal operator. Further, we give another proof of the embedding from $BV$ to $L^{n/(n-1),1}$ due to Alvino by using the usual medians.

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Yohei Tsutsui. 2024-07-25. Fractional medians and their maximal functions. https://arxiv.org/abs/2407.17700

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