Artículo
Some remarks on non-symmetric polarization
Fecha de publicación:
10/2018
Editorial:
Academic Press Inc Elsevier Science
Revista:
Journal of Mathematical Analysis and Applications
ISSN:
0022-247X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let P:Cn→C be an m-homogeneous polynomial given by P(x)=∑1≤j1≤…≤jm≤ncj1…jm xj1 …xjm . Defant and Schlüters defined a non-symmetric associated m-form LP:(Cn)m→C by LP(x(1),…,x(m))=∑1≤j1≤…≤jm≤ncj1…jm xj1 (1)…xjm (m). They estimated the norm of LP on (Cn,‖⋅‖)m by the norm of P on (Cn,‖⋅‖) times a (clogn)m2 factor for every 1-unconditional norm ‖⋅‖ on Cn. A symmetrization procedure based on a card-shuffling algorithm which (together with Defant and Schlüters’ argument) brings the constant term down to (cmlogn)m−1 is provided. Regarding the lower bound, it is shown that the optimal constant is bigger than (clogn)m/2 when n≫m. Finally, the case of ℓp-norms ‖⋅‖p with 1≤p<2 is addressed.
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Marceca, Felipe; Some remarks on non-symmetric polarization; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 466; 2; 10-2018; 1486-1498
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