Homogeneous Triebel-Lizorkin Spaces on Stratified Lie Groups

الملخص EN

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.