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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - Feb 2021|
All Science Journal Classification (ASJC) codes
- Applied Mathematics