Timeline for Estimate infinity norm with Lp and W1p norm
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2015 at 10:25 | vote | accept | user35593 | ||
| Apr 17, 2014 at 22:43 | comment | added | Delio Mugnolo | sorry, year -> here. amazing typo. | |
| Apr 17, 2014 at 18:26 | vote | accept | user35593 | ||
| Jun 29, 2015 at 10:25 | |||||
| Apr 17, 2014 at 3:36 | comment | added | Scott Armstrong | There is a very easy way to get this kind of interpolation inequality. Under these assumptions, the function is Holder continuous (with constant depending on the $W^{1,p}$ seminorm). If its maximum is 1, then you can put a Holder modulus underneath the graph of the function, centered at the point where the max occurs. When you see how much area lies under the graph of the (pth power of) this "tent", you get a lower bound for the L^p norm of the function. I believe you get something close to the conjectures inequality in the question, but I am too lazy to check how the exponents work out. | |
| Apr 17, 2014 at 2:54 | comment | added | Deane Yang | Delio, yes, you're right. I didn't notice the dimension. | |
| Apr 16, 2014 at 23:08 | comment | added | Delio Mugnolo | @Deane Yang: But $n=1$ year, isn't it? | |
| Apr 16, 2014 at 21:28 | comment | added | Deane Yang | Also, the inequality does not hold for all $p \ge 1$. $p$ must be greater than $n$. You can see this by testing the inequality with $f = r^{-\alpha}$. | |
| Apr 16, 2014 at 21:26 | comment | added | Deane Yang | Roughly, yes, but your exponents are wrong. You can always figure out what the exponents should be by considering how both sides scale when you rescale $f$ or space. The exponents do have to add up to $1$ as yours do. But when you consider what happens when you rescale space, you don't get $(p-1)/p$ and $1/p$ but $1-a$ and $a$ for another value of $a$. | |
| Apr 16, 2014 at 20:16 | answer | added | Delio Mugnolo | timeline score: 3 | |
| Apr 16, 2014 at 13:17 | history | edited | user35593 | CC BY-SA 3.0 |
deleted 25 characters in body
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| Apr 15, 2014 at 8:15 | history | asked | user35593 | CC BY-SA 3.0 |