A note on weighted Besov-type and Triebel-Lizorkin-type spaces (Q1951092)

Summary: Let \(s, \tau \in \mathbb R\), \(q \in (0, \infty]\), and \(\omega\) be in the class \(A_\infty\) of Muckenhoupt. We introduce the weighted Besov-type spaces \(\dot{B}^{s, \tau}_{p, q, \omega}(\mathbb R^n)\) and the weighted Triebel-Lizorkin-type spaces \(\dot{F}^{s, \tau}_{p, q, \omega}(\mathbb R^n)\) for \(p \in (0, \infty)\) and then we establish the \(\varphi\)-transform characterizations of these new spaces in the sense of Frazier and Jawerth.