Besov spaces on spaces of homogeneous type and fractals
Tom 156 / 2003
Studia Mathematica 156 (2003), 15-30
MSC: Primary 46E35; Secondary 42B35, 43A99.
DOI: 10.4064/sm156-1-2
Streszczenie
Let ${\mit \Gamma }$ be a compact $d$-set in ${\mathbb R}^n$ with $0< d\le n$, which includes various kinds of fractals. The author shows that the Besov spaces $B^s_{pq}({\mit \Gamma })$ defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding ${\mit \Gamma }$ as a space of homogeneous type when $0< s< 1$, $1< p< \infty $ and $1\le q\le \infty $.
