Let χ(m,n) be the unconditional basis constant of the monomial basis , α ∈ ℕ₀ⁿ with |α| = m, of the Banach space of all m-homogeneous polynomials in n complex variables, endowed with the supremum norm on the n-dimensional unit polydisc ⁿ. We prove that the quotient of and √(n/log n) tends to 1 as n → ∞. This reflects a quite precise dependence of χ(m,n) on the degree m of the polynomials and their number n of variables. Moreover, we give an analogous formula for m-linear forms, a reformulation of our results in terms of tensor products, and as an application a solution for a problem on Bohr radii.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8386-2-2016,
author = {Andreas Defant and Pablo Sevilla-Peris},
title = {Unconditionality for m-homogeneous polynomials on $ln\_{[?]}$
},
journal = {Studia Mathematica},
volume = {233},
year = {2016},
pages = {45-55},
zbl = {06575022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8386-2-2016}
}
Andreas Defant; Pablo Sevilla-Peris. Unconditionality for m-homogeneous polynomials on $ℓⁿ_{∞}$
. Studia Mathematica, Tome 233 (2016) pp. 45-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8386-2-2016/