Triebel–Lizorkin spaces with general weights

Abstract

In this paper, we identify the duals of Triebel-Lizorkin spaces of generalized smoothness. In some particular cases these function spaces are just weighted Triebel-Lizorkin spaces. To do these, we will be working at the level of sequence spaces. The ϕ-transform characterization of these function spaces in the sense of Frazier and Jawerth, and new weighted version of vector-valued maximal inequality of Fefferman and Stein are the main tools.