  We prove that, for r>2, the r-variation and oscillation for the smooth
truncations of the Cauchy transform on Lipschitz graphs are bounded in L^p for
1<p finite. The analogous result holds for the n-dimensional Riesz transform on
n-dimensional Lipschitz graphs, as well as for other singular integral
operators with odd kernel. In particular, our results strengthen the classical
theorem on the L^2 boundedness of the Cauchy transform on Lipschitz graphs by
Coifman, McIntosh, and Meyer.
