Title: On singularity of p-energy measures among distinct values of p for some p.-c.f. self-similar sets
Abstract: As a natural Lp-type energy functional and the associated (1,p)-Sobolev space, p-energy forms (Ep,Fp) have recently been constructed on a large class of self-similar sets, and it turns out that the p-energy measure of a function u, which is the analogue of "|∇ u|^p dx'', is also an important object in view of its connections with quasiconformal geometry. In this talk, I will explain a new analytic phenomenon regarding energy measures on fractals, namely, on a class of p.-c.f. self-similar sets, the p-energy measures and q-energy measures are mutually singular for any p,q ∈(1,∞) with p≠q.
This is based on joint work with Naotaka Kajino (RIMS, Kyoto University).
