Isomorphisms between vector-valued H_p-spaces for 0

2024/09/07 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +1
Computer Science · Mathematics · #46A16 #46A35 #46A40 #46A45 (Secondary) #46B15 (Primary) 46B20 #46B42 #46B45 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2409.04866

openalex publication_date 2024/09/07 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

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 \mathbbD 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(\mathbbD,ℓ₂) for 0

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