Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| dc.contributor.author | Berná, Pablo M. | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.date.accessioned | 2019-12-20T09:14:00Z | |
| dc.date.available | 2020-02-15T00:00:10Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | 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). | en |
| dc.description.sponsorship | F. Albiac and J. L. Ansorena acknowledge the support of the grant MTM2014-53009-P (MINECO, Spain). F. Albiac was also supported by the grant MTM2016-76808-P (MINECO, Spain). P. M. Bern a was supported by a Ph.D. fellowship from the program FPI-UAM, as well as the grants MTM-2016-76566-P (MINECO, Spain) and 19368/PI/14 (Fundación Séneca, Región de Murcia, Spain). | en |
| dc.embargo.lift | 2020-02-15 | |
| dc.embargo.terms | 2020-02-15 | |
| dc.format.extent | 14 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1007/s00365-019-09466-1 | |
| dc.identifier.issn | 0176-4276 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/35932 | |
| dc.language.iso | eng | en |
| dc.publisher | Springer | en |
| dc.relation.ispartof | Constructive Approximation, 2019 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2014-53009-P/ES/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/MTM2016-76808-P/ | |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/MTM2016-76566-P/ | |
| dc.relation.publisherversion | https://doi.org/10.1007/s00365-019-09466-1 | |
| dc.rights | © Springer Science+Business Media, LLC, part of Springer Nature 2019 | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Haar basis | en |
| dc.subject | Greedy basis | en |
| dc.subject | Unconditional basis | en |
| dc.subject | Democratic basis | en |
| dc.subject | Lp spaces | en |
| dc.subject | Lebesgue-type inequalities | en |
| dc.title | Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞ | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3a702006-6ba1-41ba-93bf-ea9fee1de239 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3a702006-6ba1-41ba-93bf-ea9fee1de239 |