We consider non-negative, weak solutions to the doubly nonlinear parabolic equation \(\begin{aligned} \partial _t \left( u^q\right) -\operatorname {div}\left( |Du|^{p-2}Du\right) =0 \end{aligned}\) in the super-critical fast diffusion regime \(\displaystyle 0<p-1<q<\frac{N(p-1)}{(N-p)_+}\) . We show that when solutions vanish continuously at the Lipschitz boundary of a parabolic cylinder \(\Omega _T\) , they satisfy proper Carleson estimates. Assuming further regularity for the boundary of the domain \(\Omega _T\) , we obtain a power-like decay at the boundary and a boundary Harnack inequality.
