  In this paper we introduce and investigate new 2-microlocal Besov and
Triebel-Lizorkin space via the Littlewood-Paly decomposition. We establish
characterizations of these function spaces by the $phi$-transform, the atomic
and molecular decomposition and the wavelet decomposition. As applications we
prove boundedness of Caldeon-Zygmund operators and the pseudo-differential
operators on the function spaces. Moreover, we give characterizations via
oscillations and differences.
