论文标题
$ h_p（\ mathbb {t}）的无条件基础的唯一性
Uniqueness of unconditional basis of $H_p(\mathbb{T})\oplus\ell_{2}$ and $H_p(\mathbb{T})\oplus\mathcal{T}^{(2)}$ for $0<p<1$
论文作者
论文摘要
本文我们的目标是提高无条件基础独特性主题的艺术状态。为此，我们在一对$（\ Mathbb {x}，\ Mathbb {y}）$上建立了一般条件每个求和的无条件基础。作为我们方法的应用，我们获得了$ h_p（\ Mathbb {t}^d）\ oplus \ Mathcal \ Mathcal {t}^{（2）} $和$ h_p（\ Mathbb {t}^d） $ d \ in \ mathbb {n} $，具有独特的无条件基础（直至等价和排列）。
Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair $(\mathbb{X}, \mathbb{Y})$ formed by a quasi-Banach space $\mathbb{X}$ and a Banach space $\mathbb{Y}$ which guarantee that every unconditional basis of their direct sum $\mathbb{X}\oplus\mathbb{Y}$ splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces $H_p(\mathbb{T}^d) \oplus\mathcal{T}^{(2)}$ and $H_p(\mathbb{T}^d)\oplus\ell_2$, for $p\in(0,1)$ and $d\in\mathbb{N}$, have a unique unconditional basis (up to equivalence and permutation).
