Rosenthal's inequalities: Δ-norms and quasi-Banach symmetric sequence spaces

2019/10/28 by Yong Jiao, Jiao, Yong, Guangheng Xie +5
Mathematics · #46E30 #60G50 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1910.12482

openalex publication_date 2019/10/28 · openalex created_date 2019/11/01 · openalex updated_date 2026/07/28

Abstract

Let X be a symmetric quasi-Banach function space with Fatou property and let E be an arbitrary symmetric quasi-Banach sequence space. Suppose that (f_k)_k≥0⊂ X is a sequence of independent random variables. We present a necessary and sufficient condition on X such that the quantity ‖ ‖∑_k=0ⁿf_ke_k‖_E ‖_X admits an equivalent characterization in terms of disjoint copies of (f_k)_k=0ⁿ for every n≥ 0; in particular, we obtain the deterministic description of ‖ ‖∑ _k=0ⁿf_ke_k‖_ℓq ‖_Lp for all 0

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