Timeline for An "elementary" inequality
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2020 at 17:37 | comment | added | Giorgio Metafune | I used that $\mu$ is a probability measure to have $\|g\|_1 \le \|g\|_p$ and $f \ge 0$. | |
| Sep 5, 2020 at 17:20 | comment | added | Daniel Li | $\mu$ is indeed a probability measure in the context of the monograph. f is probability density with respect to $\mu$. But seems that it is true in general by Metafune's proof? The inequality is from (13.6) in "Dynamic to random matrix" by Erdos and Yau. | |
| Sep 5, 2020 at 10:38 | comment | added | Giorgio Metafune | This follows from $(1+x) \log (1+x)\le 2x +2/(p-1)x^p$ for $x \ge 0$ writing $0 \le f=1+g$ and integrating only where $g \ge 0$. | |
| Sep 5, 2020 at 9:04 | comment | added | Fedor Petrov | @YCor I rather expect that $\mu$ is probability measure. Because the inequality is not homogeneous with respect to $\mu$. | |
| Sep 5, 2020 at 7:03 | comment | added | YCor | You really mean $f$ a probablity density? not $\mu$? Also please quote the monograph. | |
| S Sep 5, 2020 at 7:02 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Minor formatting and Math Jaxing: I added nothing to the question, so if there's one of the reviewers with more than 2000 experience points, please reject my edit and then edit it again in order to improve the formatting of this question
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| Sep 5, 2020 at 5:44 | review | Suggested edits | |||
| S Sep 5, 2020 at 7:02 | |||||
| Sep 5, 2020 at 5:17 | history | asked | Daniel Li | CC BY-SA 4.0 |