We establish in this paper the Hardy–Littlewood–Sobolev inequalities for the Riesz potentials on Morrey spaces over commutative hypergroups. As a consequence, we are also able to get Olsen-type inequality on the same spaces. Here, the condition of upper Ahlfors n-regular by identity is assumed to obtain the inequalities.

中文翻译：

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超群上Riesz势的Hardy–Littlewood–Sobolev不等式的扩展

我们在本文中建立了交换超群上Morrey空间上Riesz势的Hardy–Littlewood–Sobolev不等式。结果，我们也能够在相同的空间上得到Olsen型不等式。在此，假设通过等式的上Ahlfors n-正则条件获得不等式。