1Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A. 2Department of Mathematics Beijing Normal University Beijing 100875 People's Republic of China
Studia Mathematica, Tome 156 (2003) no. 1, pp. 67-97
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 $p, q\le 1$ 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 ${\mathbb R}^n$.
Keywords:
norms distributions spaces homogeneous type which include fractals introduced using inhomogeneous discrete calder reproducing formulae plancherel lya inequalities spaces homogeneous type authors prove these norms characterization besov triebel lizorkin spaces introduce inhomogeneous besov triebel lizorkin spaces spaces homogeneous type moreover atomic decompositions these spaces obtained results paper even mathbb
Affiliations des auteurs :
Yongsheng Han
1
;
Dachun Yang
2
1
Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A.
2
Department of Mathematics Beijing Normal University Beijing 100875 People's Republic of China
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Yongsheng Han; Dachun Yang. Some new spaces of Besov and Triebel–Lizorkin type
on homogeneous spaces. Studia Mathematica, Tome 156 (2003) no. 1, pp. 67-97. doi: 10.4064/sm156-1-5
