  The aim of this note is twofold. Firstly, we prove an abstract version of the
Calder\'on transference principle for inequalities of admissible type in the
general commutative multilinear and multiparameter setting. Such an operation
does not increase the constants in the transferred inequalities. Secondly, we
use the last information to study a certain dichotomy arising in problems of
finding the best constants in the weak type $(1,1)$ and strong type $(p,p)$
inequalities for one-parameter ergodic maximal operators.
