Albiac Alesanco, Fernando JoséAnsorena, José L.Berná, Pablo M.2019-12-202020-02-1520190176-427610.1007/s00365-019-09466-1https://academica-e.unavarra.es/handle/2454/35932Our 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).14 p.application/pdfeng© Springer Science+Business Media, LLC, part of Springer Nature 2019Haar basisGreedy basisUnconditional basisDemocratic basisLp spacesLebesgue-type inequalitiesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess