Some new spaces of Besov and Triebel–Lizorkin type on homogeneous spaces

Volume 156 / 2003

Yongsheng Han, Dachun Yang Studia Mathematica 156 (2003), 67-97 MSC: Primary 42B35; Secondary 42B25, 46E35, 43A99. DOI: 10.4064/sm156-1-5


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 ${\mathbb R}^n$.


  • Yongsheng HanDepartment of Mathematics
    Auburn University
    Auburn, AL 36849-5310, U.S.A.
  • Dachun YangDepartment of Mathematics
    Beijing Normal University
    Beijing 100875
    People's Republic of China

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