Quantitative Hardy--Littlewood maximal inequalities and Wiener--Stein theorem on p.c.f. fractals

Long Huang, Jinjun Li, Xiaofeng Wang

Let $K\subset {\mathbb{R}}^d$ be a post-critically finite (p.c.f.) self-similar set with Hausdorff dimension $s$, and $\hat{I}¼$ be a self-similar probability measure supported on $K$. Let…