Albiac Alesanco, Fernando José

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https://academica-e.unavarra.es/handle/2454/48472

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Albiac Alesanco

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Fernando José

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0001-7051-9279

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88452

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504

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Author: Albiac Alesanco, Fernando José × Subject: Haar basis ×

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    PublicationOpen Access
    Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞
    (Springer, 2019) Albiac Alesanco, Fernando José; Ansorena, José L.; Berná, Pablo M.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
    Our aim in this paper is to attain a sharp asymptotic estimate for the greedy constant Cg[H(p), Lp] of the (normalized) Haar system H(p) in Lp[0 , 1] for 1 < p < ∞. We will show that the super-democracy constant of H(p) in Lp[0 , 1] grows as p∗= max { p, p/ (p- 1) } as p∗ goes to ∞. Thus, since the unconditionality constant of H(p) in Lp[0 , 1] is p∗- 1 , the well-known general estimates for the greedy constant of a greedy basis obtained from the intrinsic features of greediness (namely, democracy and unconditionality) yield that p∗≲Cg[H(p),Lp]≲(p∗)2. Going further, we develop techniques that allow us to close the gap between those two bounds, establishing that, in fact, Cg[H(p), Lp] ≈ p∗. Our work answers a question that was raised by Hytonen (2015).