Porosity and the lp-conjecture for semigroups

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dc.contributor.authorAkbarbaglu, I.
dc.contributor.authorMaghsoudi, S.
dc.contributor.authorSeoane-Sepúlveda, Juan B.
dc.date.accessioned2023-06-18T06:50:55Z
dc.date.available2023-06-18T06:50:55Z
dc.date.issued2016
dc.description.abstractIn this paper, we consider the size of the set ( f, g) ∈ p(S) × q (S) : ∃ x ∈ S, | f |∗|g|(x) < ∞ , where p ∈ (1, +∞), q ∈ (0, +∞], and S stands for a discrete semigroup. In particular, we prove that if S is an infinite discrete semigroup, p ∈ (1, +∞), q ∈ (1, +∞] with 1/p+1/q < 1, then the set ( f, g) ∈ p(S)×q (S) : | f |∗|g| ∈ ∞(S) is a σ-c-lower porous set in p(S)×q (S)for some c > 0. By means of this notion of porosity we also provide a strengthening of a famous result by Rajagopalan on the p-conjecture.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/36456
dc.identifier.doihttp://dx.doi.org. 10.1007/s13398-014-0215-1
dc.identifier.issn15787303
dc.identifier.officialurlhttp://link.springer.com/article/10.1007/s13398-014-0215-1
dc.identifier.urihttps://hdl.handle.net/20.500.14352/24391
dc.issue.number1
dc.journal.titleRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
dc.language.isoeng
dc.page.final16
dc.page.initial7
dc.publisherSpringer Milan
dc.rights.accessRightsrestricted access
dc.subject.cdu517.98
dc.subject.keywordLebesgue space
dc.subject.keywordσ-c-Lower porous set
dc.subject.keywordSemigroup
dc.subject.keywordConvolution
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titlePorosity and the lp-conjecture for semigroups
dc.typejournal article
dc.volume.number110
dspace.entity.typePublication
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