IUMJ

Title: Energy measures of harmonic functions on the Sierpinski gasket

Authors: Ching wei Ho, Renee Bell and Robert S. Strichartz

Issue: Volume 63 (2014), Issue 3, 831-868

Abstract:

We study energy measures on SG based on harmonic functions. We characterize the positive energy measures through studying the bounds of Radon-Nikodym derivatives with respect to the Kusuoka measure. We prove a limited continuity of the derivative on the graph $V_{*}$, and express the average value of the derivative on a whole cell as a weighted average of the values on the boundary vertices. We also prove some characterizations and properties of the weights.