论文标题
部分可观测时空混沌系统的无模型预测
On the function spaces of general weights
论文作者
论文摘要
本文的目的是双重的。首先，我们将besov spaces $ \ dot {b} _ { $ \ dot {f} _ {p，q}（\ mathbb {r}^{n}，\ {t_ {k} \}）$ for $ q = \ infty $。其次，根据$ p $ - 加热权重序列$ \ {t_ {k} \} $的一些合适假设\ dot {a} _ { \ end {equation*}在等效的准核心意义上，$ \ dot {a} $ $ \ in \ {\ dot {b}，\ dot {f} \} $。此外，我们发现了空间巧合的必要条件，$ \ dot {a} _ {p，q}（\ mathbb {r}^{n}，t_ {i}），i \ in \ in \ in \ in \ {1,2 \} $。
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 \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 $\dot{A}$ $\in \{\dot{B},\dot{F}\}$. Moreover, we find a necessary and sufficient conditions for the coincidence of the spaces $\dot{A}_{p,q}(\mathbb{R}^{n},t_{i}),i\in \{1,2\}$.
