Pointwise localization and sharp weighted bounds for Rubio de Francia square functions
Let Hωf be the Fourier restriction of f ∈ L2 (R) to an interval ω ⊂ R. If Ω is an arbitrary collection of pairwise disjoint intervals, the square function of {Hωf : ω ∈ Ω} is termed the Rubio de Francia square function T Ω RF. This article proves a pointwise bound for T Ω RF by a sparse operator inv...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:318135 |
| Acesso em linha: | https://ddd.uab.cat/record/318135 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922510 |
| Access Level: | acceso abierto |
| Palavra-chave: | Rubio de Francia square function Sparse domination Sparse square functions Exponential square integrability Sharp weighted bounds Time-frequency analysis Localization principles |
| Resumo: | Let Hωf be the Fourier restriction of f ∈ L2 (R) to an interval ω ⊂ R. If Ω is an arbitrary collection of pairwise disjoint intervals, the square function of {Hωf : ω ∈ Ω} is termed the Rubio de Francia square function T Ω RF. This article proves a pointwise bound for T Ω RF by a sparse operator involving local L2 -averages. A pointwise bound for the smooth version of T Ω RF by a sparse square function is also proved. These pointwise localization principles lead to quantified Lp(w), p. |
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