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Optimal exponents in weighted estimates without examples


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dc.creator Luque Martínez, Teresa es
dc.creator Pérez Moreno, Carlos es
dc.creator Rela, Ezequiel 2016-06-29T12:07:36Z 2016-06-29T12:07:36Z 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.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 *
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.identifier.doi 10.4310/MRL.2015.v22.n1.a10 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.contributor.funder Ministerio de Ciencia e Innovación (MICIN). España
dc.contributor.funder Junta de Andalucía
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