  In this note, we show that the strong Viterbo conjecture holds true on any
convex toric domain, and that the Viterbo's volume-capacity conjecture holds
for the product of a $1$-unconditional convex body $A\subset\mathbb{R}^{n}$ and
its polar. We also give a direct calculus proof of the symmetric Mahler
conjecture for $l_p$-balls.
