The aim of this paper is twofold. Firstly, we establish the -transform characterizations of the Besov spaces { {B}, ₐ} ({R^n}, \ {{t₊}\}) and the Triebel–Lizorkin spaces { {F}, ₐ} ({R^n}, \ {{t₊}\}) for q =, in the sense of Frazier and Jawerth. Secondly, under some suitable assumptions on the p -admissible weight sequence \ {{t₊}\}, we prove that { {A}, ₐ} ({R^n}, \ {{t₊}\}) = { {A}, ₐ} ({R^n}, {t₉}), j Z, in the sense of equivalent quasi-norms, with A \ {B, F\}. Moreover, we find a necessary and sufficient conditions for the coincidence of the spaces { {A}, ₐ} ({R^n}, {t₈}), i \ 1, 2\.
Douadi Drihem (Mon,) studied this question.