Timeline for integration by parts for fractional laplacian formula for a larger class of functions
Current License: CC BY-SA 4.0
3 events
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| Jul 4, 2018 at 9:09 | comment | added | sadiaz | Thank for the help. Thats exactly what I was looking for. | |
| Jul 3, 2018 at 8:28 | comment | added | Mateusz Kwaśnicki | The formula is valid for $C_c^\infty$ functions, and then it can be extended continuously to $(f, g) \in \mathcal{D}_X \times \mathcal{D}_Y$ whenever $C_c^\infty$ is the core of $(-\Delta)^s$ on $X$ (with domain $\mathcal{D}_X$) and on $Y$ (with domain $\mathcal{D}_Y$), and $Y$ is continuously embedded into $X^*$ (perhaps with a weak* topology in $X^*$). Therefore, $X$ can be any of the $L^p$ spaces ($p \in (1, \infty)$), with $Y = X^*$, or a $C_0$ space, with, say, $Y = L^1$. Is that what you need? If yes, would you like a more detailed answer? | |
| Jul 3, 2018 at 6:40 | history | asked | sadiaz | CC BY-SA 4.0 |