Carleson embedding theorem for an exponential Bergman space on the unit ball

We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of integral operators, Ces\`{a}ro operators and Toeplitz operators, is given using the Carleson measure (or vanishing Carleson measure) characterization.