dc.contributor.author Beltran, D. dc.contributor.author Madrid, J. dc.date.accessioned 2019-07-26T18:58:15Z dc.date.available 2019-07-26T18:58:15Z dc.date.issued 2019 dc.identifier.uri http://hdl.handle.net/20.500.11824/995 dc.description.abstract We establish continuity mapping properties of the non-centered fractional maximal operator $M_{\beta}$ in the endpoint input space $W^{1,1}(\mathbb{R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. More precisely, we prove that for $q=d/(d-\beta)$ the map $f \mapsto |\nabla M_\beta f|$ is continuous from $W^{1,1}(\mathbb{R}^d)$ to $L^{q}(\mathbb{R}^d)$ for $0 < \beta < 1$ if $f$ is radial and for $1 \leq \beta < d$ for general $f$. The results for $1\leq \beta < d$ extend to the centered counterpart $M_\beta^c$. Moreover, if $d=1$, we show that the conjectured boundedness of that map for $M_\beta^c$ implies its continuity. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Maximal function en_US dc.subject Sobolev spaces en_US dc.subject Continuity en_US dc.title Endpoint Sobolev continuity of the fractional maximal function in higher dimensions en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation.projectID ES/1PE/SEV-2017-0718 en_US dc.relation.projectID EUS/BERC/BERC.2018-2021 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/submittedVersion en_US
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