分数中值及其最大函数

Yohei Tsutsui
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引用次数: 0

摘要

本文介绍了分数中值,给出了所有分数中值集合的非递增重排表达式,然后研究了由这些中值定义的分数最大算子的映射性质。事实证明,我们的最大算子是一个比通常的分数最大算子更平滑的算子。此外,我们还利用通常的中值给出了阿尔维诺提出的从 $BV$ 到 $L^{n/(n-1),1}$ 的嵌入的另一个证明。
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Fractional medians and their maximal functions
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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