Chain rule for weighted Triebel-Lizorkin spaces

In this paper we establish a fractional chain rule in the setting of weighted Triebel-Lizorkin spaces. Notably, this provides a fractional chain rule for weighted Lebesgue spaces, $L^p\left(w\right)$, for $p\le 1$. Additionally, an explicit relationship between the smoothness index, integrability index, and the choice of weights is determined.