dc.creator | Lerner, Andrei K. | es |
dc.creator | Pérez Moreno, Carlos | es |
dc.date.accessioned | 2016-06-16T07:37:05Z | |
dc.date.available | 2016-06-16T07:37:05Z | |
dc.date.issued | 2007 | |
dc.identifier.citation | Lerner, A.K. y Pérez Moreno, C. (2007). A new characterization of the Muckenhoupt Ap weights through an extension of the Lorentz-Shimogaki theorem. Indiana University Mathematics Journal, 56 (6), 2697-2722. | |
dc.identifier.issn | 0022-2518 | es |
dc.identifier.issn | 1943-5258 | es |
dc.identifier.uri | http://hdl.handle.net/11441/42373 | |
dc.description.abstract | Given any quasi-Banach function space X over Rn it is defined an index αX that coincides with the upper Boyd index αX when the space X is rearrangement-invariant. This new index is defined by means of the local maximal operator mλf . It is shown then that the Hardy-Littlewood maximal operator M is bounded on X if and only if αX < 1 providing an extension of the classical theorem of Lorentz and Shimogaki for rearrangement-invariant X. As an application it is shown a new characterization of the Muckenhoupt
Ap class of weights: u ∈ Ap if and only if for any ε > 0 there is a constant c such that for any cube Q and any measurable subset E ⊂ Q, |E| |Q| logε
|Q| |E| ≤ c u(E) u(Q)!1/p. The case ε = 0 is false corresponding to the class Ap,1. Other applications are given, in particular within the context of the
variable Lp spaces. | es |
dc.description.sponsorship | Ministerio de Educación y Ciencia | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Indiana University | es |
dc.relation.ispartof | Indiana University Mathematics Journal, 56 (6), 2697-2722. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | maximal operators | es |
dc.subject | rearrangement-invariant spaces | es |
dc.subject | Muckenhoupt weights | es |
dc.title | A new characterization of the Muckenhoupt Ap weights through an extension of the Lorentz-Shimogaki theorem | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | MTM2006-05622 | es |
dc.relation.publisherversion | http://dx.doi.org/10.1512/iumj.2007.56.3112 | es |
dc.identifier.doi | 10.1512/iumj.2007.56.3112 | es |
idus.format.extent | 26 p. | es |
dc.journaltitle | Indiana University Mathematics Journal | es |
dc.publication.volumen | 56 | es |
dc.publication.issue | 6 | es |
dc.publication.initialPage | 2697 | es |
dc.publication.endPage | 2722 | es |
dc.relation.publicationplace | Bloomington | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/42373 | |
dc.contributor.funder | Ministerio de Educación y Ciencia (MEC). España | |