  In recent work with Berndtsson and Rubinstein, a notion of $L^p$-polarity was
introduced, with classical polarity recovered in the limit $p\to\infty$, and
$L^1$-polarity closely related to Bergman kernels of tube domains. A Santal\'o
inequality for the $L^p$-polar was proved for symmetric convex bodies. The aim
of this article is to remove the symmetry assumption. Thus, an $L^p$-Santal\'o
inequality holds for any convex body after translation by the $L^p$-Santal\'o
point. As a corollary, this yields an optimal upper bound on Bergman kernels of
tube domains. The proof is by Steiner symmetrization, but unlike the symmetric
case, a careful translation of the body is required before each symmetrization.
