In my FEM lecture notes we make in several theorems use of the so called invers inequality for polynomials:
Let $\omega\subset \mathbb{R}^d$ and let $p_h\in \mathbb{P}^k(\omega,\mathbb{R})$ a polynomial of order $k$ defined on $\omega$, then the following inverse inequality holds: \begin{align} ||p_h||_{L^2{(\partial\omega)}}\leq C \frac{k}{\sqrt{diam(\omega)}}||p_h||_{L^2{(\omega)}} \end{align} where $C$ is a positiv constant that dosent depend on the size of $\omega$.
I would like to know how to show this result.