2-microlocal spaces associated with Besov type and Triebel–Lizorkin type spaces.

In this paper we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel–Lizorkin type spaces. We establish characterizations of these function spaces via the φ –transform, the atomic and molecular decomposition and the wavelet decomposition. As applications we consider boundedness of the Calder o ´ n–Zygmund operator and the pseudo–differential operator on the function spaces. [ABSTRACT FROM AUTHOR]