Asymptotics of the quantization errors for in-homogeneous self-similar measures supported on self-similar sets

We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈（0, ∞） and determine its exact value ξr. Furthermore, we show that,the ξr-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient.