dc.creator | Hagelstein, Paul | es |
dc.creator | Luque Martínez, Teresa | es |
dc.creator | Parissis, Ioannis | es |
dc.date.accessioned | 2016-11-30T08:38:51Z | |
dc.date.available | 2016-11-30T08:38:51Z | |
dc.date.issued | 2015-11 | |
dc.identifier.citation | Hagelstein, P., Luque Martínez, T.E. y Parissis, I. (2015). Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases. Transactions of the American Mathematical Society, 367 (11), 7999-8032. | |
dc.identifier.issn | 0002-9947 | es |
dc.identifier.issn | 1088-6850 | es |
dc.identifier.uri | http://hdl.handle.net/11441/49377 | |
dc.description.abstract | Let B be a homothecy invariant collection of convex sets in Rn. Given a measure μ, the associated weighted geometric maximal operator MB,μ
is defined by MB,μf(x) := sup x∈B∈B 1/μ(B) B |f|dμ. It is shown that, provided μ satisfies an appropriate doubling condition with respect to B and ν is an arbitrary locally finite measure, the maximal operator MB,μ is bounded on Lp(ν) for sufficiently large p if and only if it satisfies a Tauberian condition of the form ν x ∈ Rn : MB,μ(1E)(x) > 1 / 2 ≤ cμ,νν(E). As a consequence of this result we provide an alternative characterization of the class of Muckenhoupt weights A∞,B for homothecy invariant Muckenhoupt bases B consisting of convex sets. Moreover, it is immediately seen that the strong maximal function MR,μ, defined with respect to a product-doubling measure μ, is bounded on Lp(ν) for some p > 1 if and only if ν x ∈ Rn : MR,μ(1E)(x) > 1 /
2 ≤ cμ,νν(E) holds for all ν-measurable sets E in Rn. In addition, we discuss applications in differentiation theory, in particular proving that a μ-weighted homothecy invariant basis of convex sets satisfying appropriate doubling and Tauberian conditions must differentiate L∞(ν). | es |
dc.description.sponsorship | Simons Foundation | es |
dc.description.sponsorship | Ministerio de Economía y Competitividad | es |
dc.description.sponsorship | Academy of Finland | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | American Mathematical Society | es |
dc.relation.ispartof | Transactions of the American Mathematical Society, 367 (11), 7999-8032. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Strong maximal function | es |
dc.subject | Tauberian condition | es |
dc.subject | Muckenhoupt weight | es |
dc.title | Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/acceptedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | 208831 | es |
dc.relation.projectID | info:eu-repo/grantAgreement/MINECO/BES-2010-030264 | es |
dc.relation.projectID | 138738 | es |
dc.relation.publisherversion | http://www.ams.org/journals/tran/2015-367-11/S0002-9947-2015-06339-9/S0002-9947-2015-06339-9.pdf | es |
dc.identifier.doi | 10.1090/tran/6339 | es |
idus.format.extent | 35 p. | es |
dc.journaltitle | Transactions of the American Mathematical Society | es |
dc.publication.volumen | 367 | es |
dc.publication.issue | 11 | es |
dc.publication.initialPage | 7999 | es |
dc.publication.endPage | 8032 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/49377 | |
dc.contributor.funder | Simons Foundation | |
dc.contributor.funder | Ministerio de Economía y Competitividad (MINECO). España | |