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 \(K\oplus _p K^{\circ }\) $K{\oplus }_p{K}^{\circ }$ of the centrally symmetric convex domain K and it’s polar \(K^{\circ }\) $K^{\circ }$ to the product \(K \times K^{\circ }\) $K\times K^{\circ }$ . The rescaling constant is sharp in some cases. Additionally, we comment about the strong Viterbo conjecture for \(K\oplus _p K^{\circ }\) $K{\oplus }_p{K}^{\circ }$ .