On the function spaces of general weights
Douadi Drihem

TL;DR
This paper characterizes certain Besov and Triebel-Lizorkin function spaces with general weights, establishing conditions for their equivalence and identifying when different weighted spaces coincide.
Contribution
It provides a characterization of weighted Besov and Triebel-Lizorkin spaces for q=∞ and proves equivalence of these spaces under specific assumptions on the weights.
Findings
Characterization of Besov and Triebel-Lizorkin spaces for q=∞
Equivalence of weighted spaces under certain conditions
Necessary and sufficient conditions for space coincidence
Abstract
The aim of this paper is twofold. Firstly, we chatacterize the Besov spaces and the Triebel-Lizorkin spaces for . Secondly, under some suitable assumptions on the -admissible weight sequence , we prove that \begin{equation*} \dot{A}_{p,q}(\mathbb{R}^{n},\{t_{k}\})=\dot{A}_{p,q}(\mathbb{R} ^{n},t_{j}),\quad j\in \mathbb{Z}, \end{equation*} in the sense of equivalent quasi-norms, with . Moreover, we find a necessary and sufficient conditions for the coincidence of the spaces .
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Advanced Mathematical Physics Problems
