Korevaar-Schoen spaces on Sierpi\'nski carpets

TL;DR

This paper establishes $L^p$-regularity inequalities on generalized Sierpiński carpets, addressing an open question and utilizing a technique inspired by Alf Jonsson's 1996 idea.

Contribution

It provides the first proof of $L^p$-regularity inequalities on generalized Sierpiński carpets, advancing understanding of analysis on fractal spaces.

Findings

Proves $L^p$-regularity inequalities on generalized Sierpiński carpets

Answers an open question posed by Fabrice Baudoin

Introduces a technique based on Alf Jonsson's 1996 idea

Abstract

We prove that certain $L^p$-regularity functional inequality holds on \emph{generalized Sierpi\'nski 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.