dc.creator | Luque Martínez, Teresa | es |
dc.creator | Pérez Moreno, Carlos | es |
dc.creator | Rela, Ezequiel | |
dc.date.accessioned | 2016-06-29T12:07:36Z | |
dc.date.available | 2016-06-29T12:07:36Z | |
dc.date.issued | 2015 | |
dc.identifier.citation | Pérez Moreno, C. y Rela, E. (2015). Optimal exponents in weighted estimates without examples. Mathematical Research Letters, 22 (1), 183-201. | |
dc.identifier.issn | 1073-2780 | es |
dc.identifier.uri | http://hdl.handle.net/11441/42933 | |
dc.description.abstract | t. We present a general approach for proving the optimality
of the exponents on weighted estimates. We show that if an operator T
satisfies a bound like
kT kLp(w) ≤ c [w]
β
Ap
w ∈ Ap,
then the optimal lower bound for β is closely related to the asymptotic
behaviour of the unweighted L
p
norm kT kLp(Rn) as p goes to 1 and +∞,
which is related to Yano’s classical extrapolation theorem. By combining
these results with the known weighted inequalities, we derive the
sharpness of the exponents, without building any specific example, for
a wide class of operators including maximal-type, Calder´on–Zygmund
and fractional operators. In particular, we obtain a lower bound for the
best possible exponent for Bochner-Riesz multipliers. We also present
a new result concerning a continuum family of maximal operators on
the scale of logarithmic Orlicz functions. Further, our method allows to
consider in a unified way maximal operators defined over very general
Muckenhoupt bases. | es |
dc.description.sponsorship | Ministerio de Ciencia e Innovación | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | International Press | es |
dc.relation.ispartof | Mathematical Research Letters, 22 (1), 183-201. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Muckenhoupt weights | es |
dc.subject | Calderón-Zygmund operators | es |
dc.subject | Maximal functions | es |
dc.title | Optimal exponents in weighted estimates without examples | es |
dc.type | info:eu-repo/semantics/article | es |
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 | MTM2012-30748 | es |
dc.relation.projectID | FQM-4745 | es |
dc.relation.publisherversion | http://dx.doi.org/10.4310/MRL.2015.v22.n1.a10 | |
dc.identifier.doi | 10.4310/MRL.2015.v22.n1.a10 | |
dc.contributor.group | Universidad de Sevilla. FQM-354 Análisis Real | es |
idus.format.extent | 36 p. | es |
dc.journaltitle | Mathematical Research Letters | es |
dc.publication.volumen | 22 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 183 | es |
dc.publication.endPage | 201 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/42933 | |
dc.contributor.funder | Ministerio de Ciencia e Innovación (MICIN). España | |
dc.contributor.funder | Junta de Andalucía | |