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

Abstract

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 Calderón-Zygmund operator and the pseudo-differential operator on the function spaces.

Local theory for 2‐microlocal Besov and Triebel–Lizorkin spaces of Jaffard type

“…Moreover, these new 2-microlocal spaces are very similar to the classical 2-microlocal spaces like relations between the Besov space and the Triebel-Lizorkin space. In [21], we investigated the properties and characterizations of these new 2-microlocal spaces. In this paper, we consider the local theory for these 2-microlocal spaces.…”