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DC Field | Value | Language |
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dc.contributor.author | Baena Miret, Sergi | - |
dc.contributor.author | Carro Rossell, María Jesús | - |
dc.date.accessioned | 2025-01-20T08:36:02Z | - |
dc.date.available | 2025-01-20T08:36:02Z | - |
dc.date.issued | 2023-05-15 | - |
dc.identifier.issn | 0022-1236 | - |
dc.identifier.uri | https://hdl.handle.net/2445/217655 | - |
dc.description.abstract | It 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.extent | 24 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Elsevier | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1016/j.jfa.2023.109902 | - |
dc.relation.ispartof | Journal of Functional Analysis, 2023, vol. 284, num.10 | - |
dc.relation.uri | https://doi.org/10.1016/j.jfa.2023.109902 | - |
dc.rights | cc by (c) Sergi Baena Miret et al., 2023 | - |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Anàlisi harmònica | - |
dc.subject.classification | Anàlisi funcional | - |
dc.subject.classification | Teoria d'operadors | - |
dc.subject.classification | Transformacions de Fourier | - |
dc.subject.other | Harmonic analysis | - |
dc.subject.other | Functional analysis | - |
dc.subject.other | Operator theory | - |
dc.subject.other | Fourier transformations | - |
dc.title | On weak-type (1, 1) for averaging type operators | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.date.updated | 2025-01-20T08:36:02Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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