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

Yongsheng Han, and Dachun Yang. "Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces." Studia Mathematica 156.1 (2003): 67-97. <http://eudml.org/doc/284986>.

@article{YongshengHan2003,
abstract = {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.},
author = {Yongsheng Han, Dachun Yang},
journal = {Studia Mathematica},
keywords = {space of homogeneous type; Besov spaces; Triebel-Lizorkin spaces; Littlewood-Paley function; molecule; Littlewood-Paley -function},
language = {eng},
number = {1},
pages = {67-97},
title = {Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces},
url = {http://eudml.org/doc/284986},
volume = {156},
year = {2003},
}

TY - JOUR
AU - Yongsheng Han
AU - Dachun Yang
TI - Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces
JO - Studia Mathematica
PY - 2003
VL - 156
IS - 1
SP - 67
EP - 97
AB - 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.
LA - eng
KW - space of homogeneous type; Besov spaces; Triebel-Lizorkin spaces; Littlewood-Paley function; molecule; Littlewood-Paley -function
UR - http://eudml.org/doc/284986
ER -