Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217655
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dc.contributor.authorBaena Miret, Sergi-
dc.contributor.authorCarro Rossell, María Jesús-
dc.date.accessioned2025-01-20T08:36:02Z-
dc.date.available2025-01-20T08:36:02Z-
dc.date.issued2023-05-15-
dc.identifier.issn0022-1236-
dc.identifier.urihttps://hdl.handle.net/2445/217655-
dc.description.abstractIt is known that, due to the fact that $L^{1, \infty}$ is not a Banach space, if $\left(T_j\right)_j$ is a sequence of bounded operators so that $$ T_j: L^1 \longrightarrow L^{1, \infty} $$ with norm less than or equal to $\left\|T_j\right\|$ and $\sum_j\left\|T_j\right\|<\infty$, nothing can be said about the operator $T=\sum_j T_j$. This is the origin of many difficult and open problems. However, if we assume that $$ T_j: L^1(u) \longrightarrow L^{1, \infty}(u), \quad \forall u \in A_1 $$ with norm less than or equal to $\varphi\left(\|u\|_{A_1}\right)\left\|T_j\right\|$, where $\varphi$ is a nondecreasing function and $A_1$ the Muckenhoupt class of weights, then we prove that, essentially, $$ T: L^1(u) \longrightarrow L^{1, \infty}(u), \quad \forall u \in A_1 $$ We shall see that this is the case of many interesting problems in Harmonic Analysis.-
dc.format.extent24 p.-
dc.format.mimetypeapplication/pdf-
dc.language.isoeng-
dc.publisherElsevier-
dc.relation.isformatofReproducció del document publicat a: https://doi.org/10.1016/j.jfa.2023.109902-
dc.relation.ispartofJournal of Functional Analysis, 2023, vol. 284, num.10-
dc.relation.urihttps://doi.org/10.1016/j.jfa.2023.109902-
dc.rightscc by (c) Sergi Baena Miret et al., 2023-
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.sourceArticles publicats en revistes (Matemàtiques i Informàtica)-
dc.subject.classificationAnàlisi harmònica-
dc.subject.classificationAnàlisi funcional-
dc.subject.classificationTeoria d'operadors-
dc.subject.classificationTransformacions de Fourier-
dc.subject.otherHarmonic analysis-
dc.subject.otherFunctional analysis-
dc.subject.otherOperator theory-
dc.subject.otherFourier transformations-
dc.titleOn weak-type (1, 1) for averaging type operators-
dc.typeinfo:eu-repo/semantics/article-
dc.typeinfo:eu-repo/semantics/publishedVersion-
dc.date.updated2025-01-20T08:36:02Z-
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess-
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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