Abstract

We consider Hardy inequalities on antisymmetric functions. Such inequalities have substantially better constants. We show that they depend on the lowest degree of an antisymmetric harmonic polynomial. This allows us to obtain some Caffarelli–Kohn–Nirenberg-type inequalities that are useful for studying spectral properties of Schrödinger operators.

中文翻译：

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反对称函数的哈代不等式

摘要

我们考虑反对称函数上的哈代不等式。这种不等式具有更好的常数。我们表明它们取决于反对称调和多项式的最低次数。这使我们能够获得一些 Caffarelli-Kohn-Nirenberg 类型的不等式，这些不等式对于研究薛定谔算子的谱特性很有用。