On the function spaces of general weights
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Publication:6419818
arXiv2212.03509MaRDI QIDQ6419818
Publication date: 7 December 2022
Abstract: The aim of this paper is twofold. Firstly, we chatacterize the Besov spaces $dot{B}_{p,q}(mathbb{R}^{n},{t_{k}})$ and the Triebel-Lizorkin spaces $dot{F}_{p,q}(mathbb{R}^{n},{t_{k}})$ for $q=infty $. Secondly, under some suitable assumptions on the $p$-admissible weight sequence ${t_{k}}$, we prove that �egin{equation*} dot{A}_{p,q}(mathbb{R}^{n},{t_{k}})=dot{A}_{p,q}(mathbb{R} ^{n},t_{j}),quad jin mathbb{Z}, end{equation*} in the sense of equivalent quasi-norms, with $dot{A}$ $in {dot{B},dot{F}}$. Moreover, we find a necessary and sufficient conditions for the coincidence of the spaces $dot{A}_{p,q}(mathbb{R}^{n},t_{i}),iin {1,2}$.
Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)
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