A generalization of Toeplitz operators on the Bergman space

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

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