2012/05/21 by Diana Marcela Serrano-Rodriguez, Serrano-Rodriguez, Diana Marcela
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA
paper · pdf · doi:10.48550/arxiv.1205.4735
arxiv created 2012/05/21 · arxiv updated 2012/05/23
For the scalar field \mathbbK=ℝ or ℂ, the multilinear Bohnenblust--Hille inequality asserts that there exists a sequence of positive scalars (C_\mathbbK,m)m=1∞ such that %[(∑_i1,...,im=1N|U(e_i1%,...,e_im)|(2m)/(m+1))(m+1)/(2m)≤ C_\mathbbK,msup_z1,...,zm∈\mathbbDN|U(z1,...,zm)|] for all m-linear form U:\mathbbKN×...×\mathbbK% N→\mathbbK and every positive integer N, where (ei)i=1N denotes the canonical basis of \mathbbKN and \mathbbDN represents the open unit polydisk in \mathbbKN. Since its proof in 1931, the estimates for C_\mathbbK,m have been improved in various papers. In 2012 it was shown that there exist constants (C_\mathbbK,m)m=1∞ with subexponential growth satisfying the Bohnenblust-Hille inequality. However, these constants were obtained via a complicated recursive formula. In this paper, among other results, we obtain a closed (non-recursive) formula for these constants with subexponential growth.