Timeline for Embedding for the Bourgain spaces $X^{s,b}$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2017 at 15:58 | comment | added | fedja | I meant $1+|y|$, of course :) | |
| Dec 1, 2017 at 15:48 | comment | added | fedja | For a weight $w$, you have $\mathcal F(L^2(w))\subset C^1$ if and only if $\int u(y)^2w(y)\,dy<+\infty$ implies $\int u(y)|y|\,dy<+\infty$. To figure out whether the implication holds or not is a task for business calculus students. We usually prefer to challenge them with much harder exercises like finding patient's temperature from the formula that gives the result above the boiling point of water if the patient manages to survive beyond the first day in the hospital. That one only a genius can solve, but if you can read Bourgain, the task in question should be no brainer for you ;-) | |
| Dec 1, 2017 at 2:03 | comment | added | user60665 | @fedja Does it suffice to take $b \in (1/2,1)$ to get at least $C^1$ regularity with respect to the time variable? | |
| Dec 1, 2017 at 1:57 | comment | added | fedja | Not unless $b$ is large as well. The decay at $\infty$ in the $\tau$ direction for fixed $\xi$ is controlled by $b$ only, ergo... | |
| Dec 1, 2017 at 1:45 | history | asked | user60665 | CC BY-SA 3.0 |