For $f\in \mathcal{S}(\mathbb{R}^n)$, we define the seminorm $$\|f\|_{\alpha,\beta} : = \sup_{x\in \mathbb{R}^n} |x^\alpha \partial^\beta \phi(x)|$$ but I don't quite understand the argument below after the author defined the constant $C=...$
Edit: with the Leibniz formula, we get $$\partial^\alpha (-ix)^\beta \phi(x) = \sum_{\lambda+\pi = \alpha} \frac{\alpha !}{\lambda ! \pi !} \partial^\lambda (-ix)^\beta \partial^\pi \phi(x)$$ if I want to calculate this, do I have to split it into different cases because of the term $\partial^\lambda (-ix)^\beta$ .
