dc.contributor.author Martinez-Perales J.C. en_US dc.date.accessioned 2020-04-16T19:15:00Z dc.date.available 2020-04-16T19:15:00Z dc.date.issued 2020 dc.identifier.uri http://hdl.handle.net/20.500.11824/1101 dc.description.abstract The 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 $p<1$. en_US 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. dc.description.sponsorship La Caixa grant en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.relation ES/1PE/SEV-2017-0718 en_US dc.relation ES/1PE/MTM2017-82160-C2-1-P en_US dc.relation EUS/BERC/BERC.2018-2021 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Poincaré-Sobolev inequalities en_US dc.subject self-improvement en_US dc.subject fractional inequalities en_US dc.subject weights en_US dc.title A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/acceptedVersion en_US
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