  We consider here pseudo-differential operators whose symbol $\sigma(x,\xi)$
is not infinitely smooth with respect to $x$. Decomposing such symbols into
four -sometimes five- components and using tools of paradifferential calculus,
we derive sharp estimates on the action of such pseudo-differential operators
on Sobolev spaces and give explicit expressions for their operator norm in
terms of the symbol $\sigma(x,\xi)$. We also study commutator estimates
involving such operators, and generalize or improve the so-called Kato-Ponce
and Calderon-Coifman-Meyer estimates in various ways.
