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.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||出版済み - 2月 2021|
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