On the upper and lower quantization coefficient for probability measures on multiscale Moran sets

Given a finite set of patterns, we consider the Moran sets determined by using each of these patterns with a prescribed frequency. For certain infinite product measures mu on such Moran sets, we determine the exact values of the quantization dimensions D-r(mu). We give various sufficient conditions for the D-r(mu)-dimensional upper quantization coefficient and the lower one to be positive and finite. We also construct an example to illustrate our main result. (C) 2012 Elsevier Ltd. All rights reserved.