I'm trying to understand a step in a proof. I don't know which of the prerequisites are required or even helpful for what I need, so I give you the complete situation:
Let $T \subset \mathbb{R}^n$ be bounded and convex, let $k\ge 1$ be an integer and let $a\in H^{k,\infty}(T)$. Let $w$ be a continuous function on $T$ (in my situation a polynomial of degree $2k-2$, restricted to $T$). Then, some numeric integration is performed. In particular, the following expression makes my head ache:
$\sum_{l=1}^{L}c_l\cdot(aw)(y_l)$,
where $c_l\ge 0$ and $y_l$ are points in $T$. I.e. the product funciton $aw$ is evaluated at points.
But how is this well defined? I tried to find a continuous representative of $a$ using the Sobolev embedding theorems, but all the versions of them I know of exclude the case where $p=\infty$...
Any hints or thoughts are welcome :) Thank you!