A note on the capacities of Lagrangian $p$-sum

In this short note, we construct an explicit embedding of the rescaling of the $p$-sum $K{\oplus }_p{K}^{\circ }$ of the centrally symmetric convex domain $K$ and its polar $K^{\circ }$ to the product $K\times K^{\circ }$. The rescaling constant is sharp in some cases. Additionally, we comment on the strong Viterbo conjecture for $K{\oplus }_p{K}^{\circ }$.