Homogeneous triebel-lizorkin spaces on stratified lie groups

Homogeneous triebel-lizorkin spaces with full range of parameters are introduced on stratified lie groups in terms of littlewood-paley-type decomposition. it is shown that the scale of these spaces is independent of the choice of littlewood-paley-type decomposition and the sub-laplacian used for the construction of the decomposition. some basic properties of these spaces are given. as the main result of this paper,boundedness of a class of singular integral operators on these function spaces is obtained. © 2013 guorong hu.