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 Triebel–Lizorkin spaces. We establish characterizations of these function via the $$\varphi $$ –transform, atomic molecular decomposition wavelet decomposition. As applications consider boundedness Calder $$\acute{\mathrm{o}}$$ n–Zygmund operator pseudo–differential on