Timeline for Inequality with decreasing rearrangement and non-decreasing function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 23, 2022 at 14:00 | comment | added | Shaq155 | I totally forgot about $u$. Thanks again! | |
| Nov 23, 2022 at 13:56 | comment | added | Iosif Pinelis | @Shaq155 : Just the most basic form of the Minkowski inequality will suffice here. Indeed, $L$ is the $a$-norm of $u$, whereas $u$ is an additive (even, linear) function of $\nu$. | |
| Nov 23, 2022 at 11:17 | comment | added | Shaq155 | Is it easy to show that $L$ is convex in $\nu$ by the Minkowski inequality, with which you mean that $\left[\int_{S_{2}}\left|\int_{S_{1}}F(x,y), \mu_{1}(dx)\right|^{p} \mu_{2}(dy)\right]^{\frac{1}{p}} \leq \int_{S_{1}}\left(\int_{S_{2}}|F(x,y)|^p\,\mu_{2}(dy)\right)^{\frac{1}{p}}\mu_{1}(dx)?$ | |
| Nov 22, 2022 at 23:47 | comment | added | Shaq155 | Thank you very much for your nice answer! | |
| Nov 22, 2022 at 23:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 22, 2022 at 23:11 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 22, 2022 at 22:51 | vote | accept | Shaq155 | ||
| Nov 22, 2022 at 18:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 22, 2022 at 18:38 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |