dc.creator | Hytönen, Tuomas | es |
dc.creator | Pérez Moreno, Carlos | es |
dc.date.accessioned | 2016-07-01T07:36:35Z | |
dc.date.available | 2016-07-01T07:36:35Z | |
dc.date.issued | 2015-08-01 | |
dc.identifier.citation | Hytönen, T. y Pérez Moreno, C. (2015). The L(log L)e endpoint estimate for maximal singular integral operators. Journal of Mathematical Analysis and Applications, 428 (1), 605-626. | |
dc.identifier.issn | 0022-247X | es |
dc.identifier.uri | http://hdl.handle.net/11441/42999 | |
dc.description.abstract | We prove in this paper the following estimate for the maximal operator T
∗
associated to the
singular integral operator T:
kT
∗
fkL
1,∞ (w) .
1
ǫ
Z
Rn
| f(x)| ML(log L)
ǫ
(w)(x) dx, w ≥ 0, 0 < ǫ ≤ 1.
This follows from the sharp L
p
estimate
kT
∗
fkLp
(w) . p
′
(
1
δ
)
1/p
′
kfk
L
p
(ML(log L)
p−1+δ (w)), 1 < p < ∞, w ≥ 0, 0 < δ ≤ 1.
As as a consequence we deduce that
kT
∗
fkL
1,∞ (w) . [w]A1
log(e + [w]A∞
)
Z
Rn
| f | w dx,
extending the endpoint results obtained in [LOP] A. Lerner, S. Ombrosi and C. Pérez, A1 bounds for Calderón-Zygmund operators related
to a problem of Muckenhoupt and Wheeden, Mathematical Research Letters (2009), 16,
149–156 and [HP] T. Hytönen and C. Pérez, Sharp weighted bounds involving A∞, Analysis and P.D.E. 6
(2013), 777–818. DOI 10.2140/apde.2013.6.777 to maximal singular integrals. Another
consequence is a quantitative two weight bump estimate. | es |
dc.description.sponsorship | Unión Europea | es |
dc.description.sponsorship | Ministerio de Ciencia e Innovación | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Journal of Mathematical Analysis and Applications, 428 (1), 605-626. | |
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 | Calderón–Zygmund operators | es |
dc.subject | weighted estimates | es |
dc.title | The L(log L)e endpoint estimate for maximal singular integral operators | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | MTM2012-30748 | es |
dc.relation.projectID | info:eu-repo/grantAgreement/EC/FP7/278558 | |
dc.relation.publisherversion | http://dx.doi.org/10.1016/j.jmaa.2015.03.017 | |
dc.identifier.doi | 10.1016/j.jmaa.2015.03.017 | es |
dc.contributor.group | Universidad de Sevilla. FQM-354: Análisis Real | es |
idus.format.extent | 21 p. | es |
dc.journaltitle | Journal of Mathematical Analysis and Applications | es |
dc.publication.volumen | 428 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 605 | es |
dc.publication.endPage | 626 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/42999 | |
dc.contributor.funder | European Union (UE) | |
dc.contributor.funder | Ministerio de Ciencia e Innovación (MICIN). España | |