A note on the quantization error for in-homogeneous self-similar measures

We further study the asymptotics of quantization errors for two classes of in-homogeneous self-similar measures $\mu$. We give a new sufficient condition for the upper quantization coefficient for $\mu$ to be finite. This, together with our previous work, leads to a necessary and sufficient condition for the upper and lower quantization coefficient of $\mu$ to be both positive and finite. Furthermore, we determine (estimate) the convergence order of the quantization error in case that the quantization coefficient is infinite.