Timeline for An inequality for integral on spheres
Current License: CC BY-SA 3.0
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| Mar 9, 2016 at 13:32 | comment | added | nguyen0610 | @FedorPetrov: Thank you very much. Your answer is great. In fact, I can show that $F$ is an even polynomial of order $2(k-1)$ in $r$, and can compute explicitly the coefficients, but it is not easy to use this form of $F$ to prove the inequality above. I didn't think about using Holder inequality here. A further question arises is that is $F$ decreasing in $r$? | |
| Mar 9, 2016 at 7:23 | comment | added | Fedor Petrov | for $k=1$ we have equality (since $|x|^{2-n}$ is Green function for Laplacian), for $k>1$ use power mean inequality | |
| Mar 9, 2016 at 5:19 | history | asked | nguyen0610 | CC BY-SA 3.0 |