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dc.contributor.authorMartinez-Perales J.C.en_US
dc.date.accessioned2020-04-16T19:15:00Z
dc.date.available2020-04-16T19:15:00Z
dc.date.issued2020
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1101
dc.description.abstractThe main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent self-improving result of generalized inequalities of Poincar\'e-type in the Euclidean space. The result we obtain does not need any condition on the weight, but still is not fully satisfactory, even though the result by P\'erez and Rela is obtained as a corollary of ours. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our result, we give a unified vision of weighted improved Poincar\'e-type inequalities in the Euclidean setting, which gathers both weighted improved classical and fractional Poincar\'e inequalities within an approach which avoids any representation formula. We obtain results related to some already existing results in the literature and furthermore we improve them in some aspects. Finally, we also explore analog inequalities in the context of metric spaces by means of the already known self-improving results in this setting.en_US
dc.description.sponsorshipLa Caixa granten_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.relationES/1PE/SEV-2017-0718en_US
dc.relationES/1PE/MTM2017-82160-C2-1-Pen_US
dc.relationEUS/BERC/BERC.2018-2021en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectPoincaré-Sobolev inequalitiesen_US
dc.subjectself-improvementen_US
dc.subjectfractional inequalitiesen_US
dc.subjectweightsen_US
dc.titleA note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalitiesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US


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