哈代不等式的多维弗兰克-拉普捷夫-魏德改进

Pub Date : 2024-01-11 DOI:10.1017/s0013091523000780

Prasun Roychowdhury, Michael Ruzhansky, Durvudkhan Suragan

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引用次数: 0

摘要

我们建立了超临界情况下多维欧几里得空间上经典 Lp-Hardy 不等式的新改进。最近，在[14]中，一维哈代不等式有了一种新的发展。利用函数的一些径向化技术，然后利用实线上的对称递减重排论证，给出了哈代不等式的新多维版本。还讨论了一些后果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Multidimensional Frank–Laptev–Weidl improvement of the Hardy inequality

We establish a new improvement of the classical Lp-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one-dimensional Hardy inequality. Using some radialisation techniques of functions and then exploiting symmetric decreasing rearrangement arguments on the real line, the new multidimensional version of the Hardy inequality is given. Some consequences are also discussed.

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