Timeline for Limit case of Sobolev space in $1$-D
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2020 at 18:14 | history | edited | LL 3.14 | CC BY-SA 4.0 |
added 281 characters in body
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| Apr 9, 2020 at 17:57 | comment | added | LL 3.14 | Yes you are absolutely right, there are second order differences when $n=1$ (and this is why with first order differences lead to constant functions). I edit my answer to summarize all that. | |
| Apr 9, 2020 at 15:07 | comment | added | Hannes | As a heads up, I did not claim hat the integral in the OP is exactly the $B^1_{3,3}$ seminorm. In the integer case, the usual equivalence theorem for the Besov norm (Thm. 2.5.1 in the "old Triebel") would give something like a "centered" term $f(2y-x)-2f(y)+f(x)$ in the numerator. But I figured that finiteness of the OP integral would imply finiteness of the integral with centered term, so the $B^1_{3,3}$ seminorm. | |
| Apr 8, 2020 at 17:25 | review | First posts | |||
| Apr 8, 2020 at 20:16 | |||||
| Apr 8, 2020 at 17:24 | history | answered | LL 3.14 | CC BY-SA 4.0 |