We consider higher-order interpolation inequalities of the Gagliardo–Nirenberg type with power weights for radial functions. We show that those inequalities hold for a better range of admissible power weights if we restrict ourselves to the space of radially symmetric functions. The key of the proof is to reduce the problem to a radial improvement for the weighted Hardy–Littlewood–Sobolev inequalities.

中文翻译：

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径向函数权重的高阶插值不等式

我们考虑Gagliardo-Nirenberg类型的高阶插值不等式，其径向函数具有权重。我们证明了，如果我们将自己限制在径向对称函数的空间中，那么这些不等式将在更大的容许功率权重范围内。证明的关键是将问题简化为加权Hardy–Littlewood–Sobolev不等式的径向改进。