Traces on fractals of function spaces with Muckenhoupt weights

Abstract

The present paper is devoted to the study of traces on fractals of weighted Besov spaces $B^s_{pq}({\mathbb{R}}^n,w_{\varkappa}^{\Gamma})$ as well as weighted Triebel-Lizorkin spaces $F^s_{pq}({\mathbb{R}}^n,w_{\varkappa}^{\Gamma})$ with $w_{\varkappa}^{\Gamma}(x)={\rm dist}(x,\Gamma)^{\varkappa}$, where $\Gamma$ is some $d$-set, $0<d<n$, $\varkappa>-(n-d)$.