Korevaar-Schoen spaces on Sierpiński carpets

Abstract

We prove that certain $L^p$-regularity functional inequality holds on \emph{generalized Sierpiński carpets}. This gives an affirmative answer to an open question raised by Fabrice Baudoin. Our technique originates from an old idea of Alf Jonsson in 1996.

arXiv comment14 pages; Abstract rewritten; references added and updated