Timeline for Functional inequalities involving the condition $\left(\int_0^t f(x)dx\right)^2 \ge \int_0^t f(x)^3dx$
Current License: CC BY-SA 4.0
6 events
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| May 25, 2020 at 19:29 | comment | added | leo monsaingeon | Perhaps you should make this clear by editing your question? Indeed your prefactor is $<1$ for $\gamma\in(1,3)$ so just Hölder-ing the problem is suboptimal, and I have no clue about how to get there... Is the paper focussed on small $t\to 0$, on large $t\to\infty$, or on any $t$? | |
| May 25, 2020 at 18:17 | comment | added | Ivan | @leomonsaingeon, Yes, the general integral relationship is straightforward (directly applying Holder to the condition on $f(x)$). However, the constant is critical. | |
| May 25, 2020 at 11:01 | comment | added | Giorgio Metafune | @leo_monsaingeon Yes, true! Sorry, I wrote in the wrong place | |
| May 25, 2020 at 10:58 | comment | added | leo monsaingeon | @Giorgio_Metafune: I guess this is a comment for the OP's question, rather than for my answer? | |
| May 25, 2020 at 10:27 | comment | added | Giorgio Metafune | Could you post or link the paper with the assertion on the improved constant? Thank you | |
| May 25, 2020 at 9:16 | history | answered | leo monsaingeon | CC BY-SA 4.0 |