Sobolev spaces and L^p-Poincare inequalities on nested fractals
Abstract: We prove on some nested fractals scale invariant Lp-Poincaré inequalities on metric balls in the range 1≤p≤2. Our proof is based on the
development of the local Lp-theory of Korevaar-Schoen-Sobolev spaces on
fractals using heat kernels methods. Applications to scale invariant
Sobolev inequalities and to the study of maximal functions and
Hajłasz-Sobolev spaces on fractals are given. This is a joint work with Li
Chen (Louisiana State University).