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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/140150
Ver los metadatos del registro completo
id |
CONICETDig_9a4bd137b3c2033d75e1559da55ac084 |
---|---|
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 Técnicas2025-09-29T09:47:06Zoai: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:34982025-09-29 09:47:07.172CONICET 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 |
_version_ |
1844613468354772992 |
score |
13.070432 |