论文标题
$ P $ -BANACH空间中的准绿色基地的民主，并在Hardy空间中申请TGA的效率$ H_P（\ Mathbb {D}^d）$
Democracy of quasi-greedy bases in $p$-Banach spaces with applications to the efficiency of the TGA in the Hardy spaces $H_p(\mathbb{D}^d)$
论文作者
论文摘要
我们使用新的方法，特定于非局部凸的准巴纳赫空间，以调查何时以$ 0 <p <1 $为$ p $ banach空间的准绿化基础是民主的。我们获得的新技术可以特别表明，$ 0 <p <1 $的Hardy Space $ H_P（\ Mathbb {d}）$的所有准杂乱基础都是民主的，而相反，没有$ H_P（\ Mathbb {D}^d} $ d $ d $ d $ ge 2 $ solving IS [a [a n solving in [[a] raking n of quasi-greedy基础。 Albiac，J。L。Ansorena和P. Wojtaszczyk，\ textit {$ \ ell_p $ in $ \ ell_p $（$ 0 <p <1 $）是民主的}，是民主}，J。函数。肛门。 \ textbf {280}（2021），否。 7，108871，21]。还提供了我们结果在功能分析和近似理论中的其他感兴趣空间的应用。
We use new methods, specific of non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$-Banach space for $0<p<1$ are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p(\mathbb{D})$ for $0<p<1$ are democratic while, in contrast, no quasi-greedy basis of $H_p(\mathbb{D}^d)$ for $d\ge 2$ is, solving thus a problem that was raised in [F. Albiac, J. L. Ansorena, and P. Wojtaszczyk, \textit{Quasi-greedy bases in $\ell_p$ ($0<p<1$) are democratic}, J. Funct. Anal. \textbf{280} (2021), no. 7, 108871, 21]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided.
