Lower bounds for norms of products of polynomials on Lp spaces

For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on Lp(μ), whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also hold...

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Detalles Bibliográficos
Autores principales: Carando, Daniel German, Pinasco, Damián
Publicado: 2013
Materias:
Factor problem
Homogeneous polynomials
Norm inequalities
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v214_n2_p157_Carando
http://hdl.handle.net/20.500.12110/paper_00393223_v214_n2_p157_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00393223_v214_n2_p157_Carando
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spelling paper:paper_00393223_v214_n2_p157_Carando2023-06-08T15:03:33Z Lower bounds for norms of products of polynomials on Lp spaces Carando, Daniel German Pinasco, Damián Factor problem Homogeneous polynomials Norm inequalities For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on Lp(μ), whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes Sp. For p > 2 we present some estimates on the constants involved. © Instytut Matematyczny PAN, 2013. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Pinasco, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v214_n2_p157_Carando http://hdl.handle.net/20.500.12110/paper_00393223_v214_n2_p157_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 Factor problem
Homogeneous polynomials
Norm inequalities
spellingShingle Factor problem
Homogeneous polynomials
Norm inequalities
Carando, Daniel German
Pinasco, Damián
Lower bounds for norms of products of polynomials on Lp spaces
topic_facet Factor problem
Homogeneous polynomials
Norm inequalities
description For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on Lp(μ), whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes Sp. For p > 2 we present some estimates on the constants involved. © Instytut Matematyczny PAN, 2013.
author Carando, Daniel German
Pinasco, Damián
author_facet Carando, Daniel German
Pinasco, Damián
author_sort Carando, Daniel German
title Lower bounds for norms of products of polynomials on Lp spaces
title_short Lower bounds for norms of products of polynomials on Lp spaces
title_full Lower bounds for norms of products of polynomials on Lp spaces
title_fullStr Lower bounds for norms of products of polynomials on Lp spaces
title_full_unstemmed Lower bounds for norms of products of polynomials on Lp spaces
title_sort lower bounds for norms of products of polynomials on lp spaces
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v214_n2_p157_Carando
http://hdl.handle.net/20.500.12110/paper_00393223_v214_n2_p157_Carando
work_keys_str_mv AT carandodanielgerman lowerboundsfornormsofproductsofpolynomialsonlpspaces
AT pinascodamian lowerboundsfornormsofproductsofpolynomialsonlpspaces
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