  Sharp weighted estimates are obtained for vector-valued extensions of the
Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators and
Coifman-Rochberg-Weiss commutator. Those estimates will rely upon suitable
pointwise estimates in terms of sparse operators. We also prove some new
results for the $C_p$ classes introduced by Muckenhoupt and later extended by
Sawyer, in particular we extend the result to the full expected range $p > 0$,
to the weak norm, to other operators and to the their vector-valued extensions.
