Triebel–Lizorkin spaces with general weights

Abstract

In this paper, the author introduces Triebel–Lizorkin spaces with general smoothness. We present the $$\varphi$$ -transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. Also, we establish the smooth atomic and molecular decomposition of these function spaces. To do these we need a generalization of some maximal inequality to the case of general weights.