{"title":"Isomorphisms between vector-valued $H_p$-spaces for $0","authors":"Fernando Albiac, Jose L. Ansorena","doi":"arxiv-2409.04866","DOIUrl":null,"url":null,"abstract":"The aim of this paper is twofold. On the one hand, we manage to identify\nBanach-valued Hardy spaces of analytic functions over the disc $\\mathbb{D}$\nwith other classes of Hardy spaces, thus complementing the existing literature\non the subject. On the other hand, we develop new techniques that allow us to\nprove that certain Hilbert-valued atomic lattices have a unique unconditional\nbasis, up to normalization, equivalence and permutation. Combining both lines\nof action we show that that $H_p(\\mathbb{D},\\ell_2)$ for $0<p<1$ has a unique\natomic lattice structure. The proof of this result relies on the validity of\nsome new lattice estimates for non-locally convex spaces which hold an\nindependent interest.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04866","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is twofold. On the one hand, we manage to identify
Banach-valued Hardy spaces of analytic functions over the disc $\mathbb{D}$
with other classes of Hardy spaces, thus complementing the existing literature
on the subject. On the other hand, we develop new techniques that allow us to
prove that certain Hilbert-valued atomic lattices have a unique unconditional
basis, up to normalization, equivalence and permutation. Combining both lines
of action we show that that $H_p(\mathbb{D},\ell_2)$ for $0
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