Timeline for Show that if $a$ belongs to the symbol class $S^m_{\rho , \delta}$ for $\rho > 1$, then in fact $a \in S^{-\infty}$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2017 at 18:09 | comment | added | Fan Zheng | Why do you multiply a by $\theta_0$? You don't need to do that. | |
| Jan 9, 2017 at 14:23 | comment | added | JZS | @FanZheng---Thank you, I see where you are going with this idea. It is enough to just show that we can get $|a(x, \theta) | \le C(1 + |\theta|)^{m - \varepsilon}$. But I'm having trouble deciding how to appropriately express $a(x,\theta)$ in terms of one if its partial derivatives. The best I have got so far is setting $\theta_0 = |\theta_0| \omega_0$ with $|\omega_0| = 1$ and then writing $|\theta_0| a(x, \theta_0) = \int_0^{|\theta_0|} \partial_r(r a(x, r \omega_0) )dr$, but when I use the product rule and estimate the integral, it doesn't appear that my estimates will work out. | |
| Jan 9, 2017 at 2:01 | comment | added | Fan Zheng | Use induction. If you can reduce the exponent a little, then you can reduce it as much as you want | |
| Jan 8, 2017 at 20:20 | history | asked | JZS | CC BY-SA 3.0 |