{"title":"$0 的矢量值 $H_p$ 空间之间的同构关系","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":"{\"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}","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}
Isomorphisms between vector-valued $H_p$-spaces for $0
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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