Let Γ be a compact d-set in ℝⁿ with 0 < d ≤ n, which includes various kinds of fractals. The author shows that the Besov spaces 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 Γ as a space of homogeneous type when 0 < s < 1, 1 < p < ∞ and 1 ≤ q ≤ ∞.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-2,
author = {Dachun Yang},
title = {Besov spaces on spaces of homogeneous type and fractals},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {15-30},
zbl = {1023.46035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-2}
}
Dachun Yang. Besov spaces on spaces of homogeneous type and fractals. Studia Mathematica, Tome 157 (2003) pp. 15-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-2/