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dc.contributor.author
Kangwei, Li
dc.contributor.author
Pérez, Carlos
dc.contributor.author
Rivera Ríos, Israel Pablo
dc.contributor.author
Roncal, Luz
dc.date.available
2019-10-10T17:58:26Z
dc.date.issued
2019-07
dc.identifier.citation
Kangwei, Li; Pérez, Carlos; Rivera Ríos, Israel Pablo; Roncal, Luz; Weighted Norm Inequalities for Rough Singular Integral Operators; Springer; The Journal Of Geometric Analysis; 29; 3; 7-2019; 2526-2564
dc.identifier.issn
1050-6926
dc.identifier.uri
http://hdl.handle.net/11336/85550
dc.description.abstract
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals TΩ with Ω ∈ L∞(Sn-1) and the Bochner–Riesz multiplier at the critical index B(n-1)/2. More precisely, we prove qualitative and quantitative versions of Coifman–Fefferman type inequalities and their vector-valued extensions, weighted Ap- A∞ strong and weak type inequalities for 1 < p< ∞, and A1- A∞ type weak (1, 1) estimates. Moreover, Fefferman–Stein type inequalities are obtained, proving in this way a conjecture raised by the second-named author in the 1990s. As a corollary, we obtain the weighted A1- A∞ type estimates. Finally, we study rough homogenous singular integrals with a kernel involving a function Ω ∈ Lq(Sn-1) , 1 < q< ∞, and provide Fefferman–Stein inequalities too. The arguments used for our proofs combine several tools: a recent sparse domination result by Conde–Alonso et al. (Anal PDE 10(5):1255–1284, 2017), results by the first author (Collect Math 68:129–144, 2017), suitable adaptations of Rubio de Francia algorithm, the extrapolation theorems for A∞ weights (Cruz-Uribe et al. in J Funct Anal 213:412–439, 2004, Curbera et al. in Adv Math 203:256–318, 2006), and ideas contained in previous works by Seeger (J Am Math Soc 9:95–105 1996) and Fan and Sato (Tohoku Math J 53:265–284, 2001).
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
FEFFERMAN–STEIN INEQUALITIES
dc.subject
ROUGH OPERATORS
dc.subject
RUBIO DE FRANCIA ALGORITHM
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SPARSE OPERATORS
dc.subject
WEIGHTS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Weighted Norm Inequalities for Rough Singular Integral Operators
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-10-09T14:16:42Z
dc.identifier.eissn
1559-002X
dc.journal.volume
29
dc.journal.number
3
dc.journal.pagination
2526-2564
dc.journal.pais
Alemania
dc.description.fil
Fil: Kangwei, Li. Basque Center for Applied Mathematics; España
dc.description.fil
Fil: Pérez, Carlos. Universidad del País Vasco; España
dc.description.fil
Fil: Rivera Ríos, Israel Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad del País Vasco; España
dc.description.fil
Fil: Roncal, Luz. Basque Center for Applied Mathematics; España
dc.journal.title
The Journal Of Geometric Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs12220-018-0085-4
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s12220-018-0085-4
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1701.05170


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