Isomorphisms between vector-valued $H_p$-spaces for $0<p\le 1$ and uniqueness of unconditional structure
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| Format: | Preprint |
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2024
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| _version_ | 1866912018742640640 |
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| author | Albiac, Fernando Ansorena, Jose L. |
| author_facet | Albiac, Fernando Ansorena, Jose L. |
| contents | 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 $0<p<1$ has a unique atomic lattice structure. The proof of this result relies on the validity of some new lattice estimates for non-locally convex spaces which hold an independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_04866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphisms between vector-valued $H_p$-spaces for $0<p\le 1$ and uniqueness of unconditional structure Albiac, Fernando Ansorena, Jose L. Functional Analysis 46B15 (Primary) 46B20, 46B42, 46B45, 46A16, 46A35, 46A40, 46A45 (Secondary) 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 $0<p<1$ has a unique atomic lattice structure. The proof of this result relies on the validity of some new lattice estimates for non-locally convex spaces which hold an independent interest. |
| title | Isomorphisms between vector-valued $H_p$-spaces for $0<p\le 1$ and uniqueness of unconditional structure |
| topic | Functional Analysis 46B15 (Primary) 46B20, 46B42, 46B45, 46A16, 46A35, 46A40, 46A45 (Secondary) |
| url | https://arxiv.org/abs/2409.04866 |