Let $\mathbb{P}_k(\mathbb{R}^d)$ be the space of multivariate polynomials of degree $\le k$ defined on $\mathbb{R}^d$.
Let $Q=[0,1]^d$ and let $B(0,2)$ be the ball centred at the original with radius 2.
Using the fact that $\mathbb{P}_k(\mathbb{R}^d)$ is a finite dimensional vector space and that polynomials are real analytic functions (hence they admit unique continuation), we know
\begin{equation} c\|p \|_{L^p(Q)}\le \|p \|_{L^p(B(0,2))}\le C \|p \|_{L^p(Q)} \end{equation} for $1\le p \le \infty$, for every $p\in\mathbb{P}_k(\mathbb{R}^d)$.
I'm wondering on which parameters does $C$ depend.