New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover, atomic decompositions of these new spaces are also obtained. All the results of this paper are new even for ℝⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-5,
author = {Yongsheng Han and Dachun Yang},
title = {Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {67-97},
zbl = {1032.42025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-5}
}
Yongsheng Han; Dachun Yang. Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces. Studia Mathematica, Tome 157 (2003) pp. 67-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-5/