Timeline for Convergence rate for $L^2$ convergence
Current License: CC BY-SA 4.0
11 events
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| May 22, 2018 at 21:30 | comment | added | Iosif Pinelis | @user5678 : Thank you for your interesting comment. | |
| May 22, 2018 at 19:37 | comment | added | Scott Armstrong | By the way, you might be interested in the fact that the converse of this question is also, in a certain sense, true. That is, you can define Sobolev spaces and norms (even fractional and negative spaces, and for every exponent p) in terms of spatial averages of the function on every scale. For higher derivatives, one has to use a smoother function than a characteristic function. See for instance the appendix of math.ens.fr/~mourrat/lecturenotes.pdf | |
| May 20, 2018 at 20:11 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 20, 2018 at 20:06 | comment | added | Iosif Pinelis | Thank you Piotr. Maybe I should have written down both parts of this answer at once, rather than in two steps. :-) | |
| May 20, 2018 at 18:12 | comment | added | Piotr Hajlasz | Nice answer. I cannot vote you up twice :-( | |
| May 20, 2018 at 17:40 | comment | added | Iosif Pinelis | @Selberg : Yes, it does generalize. I have now provided this generalization as well. | |
| May 20, 2018 at 17:39 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 20, 2018 at 17:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 20, 2018 at 10:30 | vote | accept | Selberg | ||
| May 20, 2018 at 10:30 | comment | added | Selberg | thank you, but does this generalize to higher dimensions? | |
| May 20, 2018 at 3:40 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |