  If $\mu$ is a finite measure on the unit disc and $k\ge 0$ is an integer, we
study a generalization derived from Englis's work, $T_\mu^{(k)}$, of the
traditional Toeplitz operators on the Bergman space $A^2$, which are the case
$k=0$. Among other things, we prove that when $\mu\ge 0$, these operators are
bounded if and only if $\mu$ is a Carleson measure, and we obtain some
estimates for their norms.
