  For a non Archimedean local field which is not of characteristic $2$, nor an
extension of $\mathbb Q_2$, we construct a pseudo-differential calculus
covariant under a unimodular subgroup of the affine group of the field. Our
phase space is a quotient group of the covariance group. Our main result is a
generalisation on that context of the Calder\'on-Vaillancourt estimate. Our
construction can be thought as the non Archimedean version of Unterberger's
Fuchs calculus and our methods are mainly based on Wigner functions and on
coherent states transform.
