Homogeneous Triebel-Lizorkin Spaces on Stratified Lie Groups

摘要

Homogeneous Triebel-Lizorkin spaces with full range of parameters are introduced onstratified Lie groups in terms of Littlewood-Paley-type decomposition. It is shownthat the scale of these spaces is independent of the choice of Littlewood-Paley-typedecomposition 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.