On the function spaces of general weights

Douadi Drihem

Published 2022-12-07Version 1

The aim of this paper is twofold. Firstly, we chatacterize the spaces $\dot{B}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ and $\dot{F}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ for $q=\infty $. Secondly, with some suitable assumptions on the $p$-admissible weight sequences $\{t_{k}\}$ we prove that \begin{equation*} \dot{F}_{p,q}(\mathbb{R}^{n},\{t_{k}\})=\dot{F}_{p,q}(\mathbb{R}^{n},t_{j}),\quad j\in \mathbb{Z}, \end{equation*} in the sense of equivalent quasi-norms.