Poincaré inequality and Hajłasz–Sobolev spaces on nested fractals
Volume 218 / 2013
Studia Mathematica 218 (2013), 1-26
MSC: Primary 46E35; Secondary 31E05, 28A80.
DOI: 10.4064/sm218-1-1
Abstract
Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz–Sobolev spaces on nested fractals. In particular, we describe how the “weak”-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
