Timeline for Weak Lebesgue spaces and an estimate for BV functions
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2019 at 15:01 | vote | accept | Riku | ||
| Apr 21, 2019 at 10:32 | comment | added | Riku | I've asked the follow up question in a separate post: mathoverflow.net/questions/328571/…. | |
| Apr 20, 2019 at 12:24 | comment | added | Riku | I see that this example is not in $L^1_{loc}$, but can't it be decomposed in the sum of two functions $F_1,F_2$ such that $\|F_1\|_{w-L^1} \le \epsilon$ and $\|F_2\|_{L^1} \le C_\epsilon$? | |
| Apr 20, 2019 at 11:53 | comment | added | Skeeve | I doubt that $M_R Du$ can be written this way. Suppose for instance that $u$ is the Heaviside step function, $N=1$. Then $M_R Du(x) = \frac{1}{2|x|}$ if $|x|\le R$ and zero otherwise. | |
| Apr 20, 2019 at 11:17 | comment | added | Riku | That's great. I wonder what's the role of weak $L^1$ vs $L^1$ to estimate $M_R Du$. That is, I'd like to ask: $\forall \epsilon>0$ is it true that $M_R Du = F_1 + F_2$, where $\| F_1\|_{w-L^1} \le \epsilon$ and $\|F_2\|_{L^1} \le C_\epsilon$? | |
| Apr 20, 2019 at 11:11 | history | answered | Skeeve | CC BY-SA 4.0 |