  Using a representation of the discrete Hilbert transform in terms of
martingales arising from Doob $h$-processes, we prove that its $l^p$-norm,
$1<p<\infty$, is bounded above by the $L^p$-norm of the continuous Hilbert
transform. Together with the already known lower bound, this resolves the
long-standing conjecture that the norms of these operators are equal.
