Adimensional weighted Sobolev inequalities in PI spaces

Abstract

We provide a family of global weighted Sobolev inequalities and Hardy inequalities on PI spaces with possibly non-maximal volume growth. Our results apply notably to non-trivial Ahlfors regular spaces like Laakso spaces and Kleiner-Schioppa spaces.

arXiv comment30 pages. This is the third version. Typos and mistakes have been corrected, notably in the proof of Proposition 3.1