Abstract We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type inequality that takes into account both the dimensional as well as the magnetic flux contributions. Second, in the three-dimensional Euclidean space, we derive a non-trivial magnetic Hardy inequality for a magnetic field that vanishes at infinity and diverges along a plane.

中文翻译：

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奇异磁场对哈代不等式的改进

摘要 我们针对奇异磁场的两个特定选择建立了经典哈代不等式的磁性改进。首先，我们考虑所有维度的 Aharonov-Bohm 场，并建立一个尖锐的 Hardy 型不等式，该不等式同时考虑了维度和磁通量的贡献。其次，在三维欧几里得空间中，我们推导出一个非平凡的磁性哈代不等式，用于在无穷远处消失并沿平面发散的磁场。