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...

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Detalhes bibliográficos
Autores: Di Plinio, Francesco|||0000-0002-2099-8272, Flórez Amatriain, Mikel, Parissis, Ioannis|||0000-0003-3583-5553, Roncal, Luz|||0000-0003-0852-3677
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
Descrição
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.