  We consider the torsional rigidity and the principal eigenvalue related to
the $p$-Laplace operator. The goal is to find upper and lower bounds to
products of suitable powers of the quantities above in various classes of
domains. The limit cases $p=1$ and $p=\infty$ are also analyzed, which amount
to consider the Cheeger constant of a domain and functionals involving the
distance function from the boundary.
