Multilinear Marcinkiewicz-Zygmund Inequalities

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 functi...

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Detalles Bibliográficos
Publicado: 2019
Materias:
Calderón-Zygmund operators
Multilinear operators
Vector-valued inequalities
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v25_n1_p51_Carando
http://hdl.handle.net/20.500.12110/paper_10695869_v25_n1_p51_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10695869_v25_n1_p51_Carando
record_format dspace
spelling paper:paper_10695869_v25_n1_p51_Carando2023-06-08T16:04:24Z Multilinear Marcinkiewicz-Zygmund Inequalities Calderón-Zygmund operators Multilinear operators Vector-valued inequalities 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. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v25_n1_p51_Carando http://hdl.handle.net/20.500.12110/paper_10695869_v25_n1_p51_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Calderón-Zygmund operators
Multilinear operators
Vector-valued inequalities
spellingShingle Calderón-Zygmund operators
Multilinear operators
Vector-valued inequalities
Multilinear Marcinkiewicz-Zygmund Inequalities
topic_facet Calderón-Zygmund operators
Multilinear operators
Vector-valued inequalities
description 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.
title Multilinear Marcinkiewicz-Zygmund Inequalities
title_short Multilinear Marcinkiewicz-Zygmund Inequalities
title_full Multilinear Marcinkiewicz-Zygmund Inequalities
title_fullStr Multilinear Marcinkiewicz-Zygmund Inequalities
title_full_unstemmed Multilinear Marcinkiewicz-Zygmund Inequalities
title_sort multilinear marcinkiewicz-zygmund inequalities
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v25_n1_p51_Carando
http://hdl.handle.net/20.500.12110/paper_10695869_v25_n1_p51_Carando
_version_ 1768544970623418368

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