Timeline for Sobolev inequality with weight in the case $1<n\leq p$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 18 at 12:52 | answer | added | Aleksei Kulikov | timeline score: 3 | |
| Nov 18 at 11:11 | comment | added | Shaq155 | It is for some $q>p$. | |
| Nov 18 at 11:07 | history | edited | Shaq155 | CC BY-SA 4.0 |
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| Nov 18 at 10:35 | history | edited | Shaq155 | CC BY-SA 4.0 |
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| Nov 18 at 10:24 | history | edited | Shaq155 | CC BY-SA 4.0 |
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| Nov 18 at 10:15 | comment | added | Aleksei Kulikov | Regardless, it seems that taking any bump function $\varphi$ and rescaling it by $\varphi(\frac{x}{C})$ gives a contradiction for any $p > n$ (right-hand side tends to $0$, left-hand side stays bounded away from $0$), and even for $p= n$ if $\mu(\mathbb{R^n}) = \infty$. Probably for $p = n$ it is still false for any strictly positive measure $\mu$ if $n > 1$ but I don't see an immediate counterexample. | |
| Nov 18 at 10:02 | comment | added | Aleksei Kulikov | What is the assumption on $q$? Is it for all $q > p$, some $q > p$? And on what is $\mu$ allowed to depend? | |
| Nov 18 at 9:55 | history | asked | Shaq155 | CC BY-SA 4.0 |