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Carando, D.; Mazzitelli, M.; Ombrosi, S. "Multilinear Marcinkiewicz-Zygmund Inequalities" (2019) Journal of Fourier Analysis and Applications. 25(1):51-85
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Abstract:

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on ℓ r -valued extensions of linear operators. We show that for certain 1 ≤ p, q 1 , ⋯ , q m , r≤ ∞, there is a constant C≥ 0 such that for every bounded multilinear operator T:Lq1(μ1)×⋯×Lqm(μm)→Lp(ν) and functions {fk11}k1=1n1⊂Lq1(μ1),⋯,{fkmm}km=1nm⊂Lqm(μm), the following inequality holds ∥(∑k1,⋯,km|T(fk11,⋯,fkmm)|r)1/r∥Lp(ν)≤C‖T‖∏i=1m∥(∑ki=1ni|fkii|r)1/r∥Lqi(μi).In some cases we also calculate the best constant C≥ 0 satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. © 2017, Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:Multilinear Marcinkiewicz-Zygmund Inequalities
Autor:Carando, D.; Mazzitelli, M.; Ombrosi, S.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
IMAS-CONICET, Buenos Aires, Argentina
Instituto Balseiro, Universidad Nacional de Cuyo - C.N.E.A., Buenos Aires, Argentina
Departamento de Matemática, Centro Regional Universitario Bariloche, Universidad Nacional del Comahue, San Carlos de Bariloche, 8400, Argentina
Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
INMABB-CONICET, Bahía Blanca, Argentina
Palabras clave:Calderón-Zygmund operators; Multilinear operators; Vector-valued inequalities
Año:2019
Volumen:25
Número:1
Página de inicio:51
Página de fin:85
DOI: http://dx.doi.org/10.1007/s00041-017-9563-5
Título revista:Journal of Fourier Analysis and Applications
Título revista abreviado:J. Fourier Anal. Appl.
ISSN:10695869
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v25_n1_p51_Carando

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Citas:

---------- APA ----------
Carando, D., Mazzitelli, M. & Ombrosi, S. (2019) . Multilinear Marcinkiewicz-Zygmund Inequalities. Journal of Fourier Analysis and Applications, 25(1), 51-85.
http://dx.doi.org/10.1007/s00041-017-9563-5
---------- CHICAGO ----------
Carando, D., Mazzitelli, M., Ombrosi, S. "Multilinear Marcinkiewicz-Zygmund Inequalities" . Journal of Fourier Analysis and Applications 25, no. 1 (2019) : 51-85.
http://dx.doi.org/10.1007/s00041-017-9563-5
---------- MLA ----------
Carando, D., Mazzitelli, M., Ombrosi, S. "Multilinear Marcinkiewicz-Zygmund Inequalities" . Journal of Fourier Analysis and Applications, vol. 25, no. 1, 2019, pp. 51-85.
http://dx.doi.org/10.1007/s00041-017-9563-5
---------- VANCOUVER ----------
Carando, D., Mazzitelli, M., Ombrosi, S. Multilinear Marcinkiewicz-Zygmund Inequalities. J. Fourier Anal. Appl. 2019;25(1):51-85.
http://dx.doi.org/10.1007/s00041-017-9563-5