The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials

Autores
Galicer, Daniel Eric; Mansilla, Martin Ignacio; Muro, Luis Santiago Miguel
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, (∑|α|=m|aα|r)1/r≤Amp,r(n)supz∈Bℓnp∣∣P(z)∣∣. For every degree m, and a wide range of values of p,r∈[1,∞] (including any r in the case p∈[1,2], and any r and p for the 2-homogeneous case), we give the correct asymptotic behavior of these constants as n (the number of variables) tends to infinity. Remarkably, in many cases, extremal polynomials for these inequalities are not (as traditionally expected) found using classical random unimodular polynomials, and special combinatorial configurations of monomials are needed. Namely, we show that Steiner polynomials (i.e., m-homogeneous polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems), do the work for certain range of values of p,r. As a byproduct, we present some applications of these estimates to the interpolation of tensor products of Banach spaces, to the study of (mixed) unconditionality in spaces of polynomials and to the multivariable von Neumann's inequality.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Materia
Hardy-Littlewood inequalities
multivariable von Neumann?s inequality.
unconditionality in spaces ofpolynomials
unimodular polynomials
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/140150
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/140150
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomialsGalicer, Daniel EricMansilla, Martin IgnacioMuro, Luis Santiago MiguelHardy-Littlewood inequalitiesmultivariable von Neumann?s inequality.unconditionality in spaces ofpolynomialsunimodular polynomialshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, (∑|α|=m|aα|r)1/r≤Amp,r(n)supz∈Bℓnp∣∣P(z)∣∣. For every degree m, and a wide range of values of p,r∈[1,∞] (including any r in the case p∈[1,2], and any r and p for the 2-homogeneous case), we give the correct asymptotic behavior of these constants as n (the number of variables) tends to infinity. Remarkably, in many cases, extremal polynomials for these inequalities are not (as traditionally expected) found using classical random unimodular polynomials, and special combinatorial configurations of monomials are needed. Namely, we show that Steiner polynomials (i.e., m-homogeneous polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems), do the work for certain range of values of p,r. As a byproduct, we present some applications of these estimates to the interpolation of tensor products of Banach spaces, to the study of (mixed) unconditionality in spaces of polynomials and to the multivariable von Neumann's inequality.Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaWiley VCH Verlag2020-12-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/140150Galicer, Daniel Eric; Mansilla, Martin Ignacio; Muro, Luis Santiago Miguel; The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials; Wiley VCH Verlag; Mathematische Nachrichten; 293; 2; 11-12-2020; 263-2830025-584XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201800404info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201800404info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1602.01735v3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:15:58Zoai:ri.conicet.gov.ar:11336/140150instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:15:59.19CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
title The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
spellingShingle The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
Galicer, Daniel Eric
Hardy-Littlewood inequalities
multivariable von Neumann?s inequality.
unconditionality in spaces ofpolynomials
unimodular polynomials
title_short The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
title_full The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
title_fullStr The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
title_full_unstemmed The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
title_sort The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials
dc.creator.none.fl_str_mv Galicer, Daniel Eric
Mansilla, Martin Ignacio
Muro, Luis Santiago Miguel
author Galicer, Daniel Eric
author_facet Galicer, Daniel Eric
Mansilla, Martin Ignacio
Muro, Luis Santiago Miguel
author_role author
author2 Mansilla, Martin Ignacio
Muro, Luis Santiago Miguel
author2_role author
author
dc.subject.none.fl_str_mv Hardy-Littlewood inequalities
multivariable von Neumann?s inequality.
unconditionality in spaces ofpolynomials
unimodular polynomials
topic Hardy-Littlewood inequalities
multivariable von Neumann?s inequality.
unconditionality in spaces ofpolynomials
unimodular polynomials
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, (∑|α|=m|aα|r)1/r≤Amp,r(n)supz∈Bℓnp∣∣P(z)∣∣. For every degree m, and a wide range of values of p,r∈[1,∞] (including any r in the case p∈[1,2], and any r and p for the 2-homogeneous case), we give the correct asymptotic behavior of these constants as n (the number of variables) tends to infinity. Remarkably, in many cases, extremal polynomials for these inequalities are not (as traditionally expected) found using classical random unimodular polynomials, and special combinatorial configurations of monomials are needed. Namely, we show that Steiner polynomials (i.e., m-homogeneous polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems), do the work for certain range of values of p,r. As a byproduct, we present some applications of these estimates to the interpolation of tensor products of Banach spaces, to the study of (mixed) unconditionality in spaces of polynomials and to the multivariable von Neumann's inequality.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
description Let Amp,r(n) be the best constant that fulfills the following inequality: for every m-homogeneous polynomial P(z)=∑|α|=maαzα in n complex variables, (∑|α|=m|aα|r)1/r≤Amp,r(n)supz∈Bℓnp∣∣P(z)∣∣. For every degree m, and a wide range of values of p,r∈[1,∞] (including any r in the case p∈[1,2], and any r and p for the 2-homogeneous case), we give the correct asymptotic behavior of these constants as n (the number of variables) tends to infinity. Remarkably, in many cases, extremal polynomials for these inequalities are not (as traditionally expected) found using classical random unimodular polynomials, and special combinatorial configurations of monomials are needed. Namely, we show that Steiner polynomials (i.e., m-homogeneous polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems), do the work for certain range of values of p,r. As a byproduct, we present some applications of these estimates to the interpolation of tensor products of Banach spaces, to the study of (mixed) unconditionality in spaces of polynomials and to the multivariable von Neumann's inequality.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/140150
Galicer, Daniel Eric; Mansilla, Martin Ignacio; Muro, Luis Santiago Miguel; The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials; Wiley VCH Verlag; Mathematische Nachrichten; 293; 2; 11-12-2020; 263-283
0025-584X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/140150
identifier_str_mv Galicer, Daniel Eric; Mansilla, Martin Ignacio; Muro, Luis Santiago Miguel; The sup‐norm vs. the norm of the coefficients: equivalence constants for homogeneous polynomials; Wiley VCH Verlag; Mathematische Nachrichten; 293; 2; 11-12-2020; 263-283
0025-584X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201800404
info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201800404
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1602.01735v3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Wiley VCH Verlag
publisher.none.fl_str_mv Wiley VCH Verlag
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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