  We state and prove estimates for the local boundedness of subsolutions of
non-local, possibly degenerate, parabolic integro-differential equations of the
form \begin{equation*}
  \partial_tu(x,t)+\mbox{P.V.}\int\limits_{\mathbb R^n}K(x,y,t) |u(x,t)-u(y,t)
|^{p-2}(u(x,t)-u(y,t))\, dy,\end{equation*} $(x,t)\in\mathbb R^n\times\mathbb
R$, where $\mbox{P.V.} $ means in the principle value sense, $p\in (1,\infty)$
and the kernel obeys $K(x,y,t)\approx |x-y |^{n+ps}$ for some $s\in (0,1)$,
uniformly in $(x,y,t)\in\mathbb R^n\times \mathbb R^n\times\mathbb R$.

Analysis of PDEs