[EN] The Bohr–Bohnenblust–Hille theorem states that the width of the strip in the complex plane on which an
ordinary Dirichlet series P
n
ann
−s
converges uniformly but not absolutely is less than or equal to 1
2
, ...
[EN] We study extendibility of diagonal multilinear operators from l(p) to l(p) spaces. We determine the values of and for which every diagonal -linear operator is extendible, and those for which the only extendible ones ...
[EN] We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st. and cotype, and spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get ...
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
Carando, Daniel; Defant, Andreas; García, Domingo; Maestre, Manuel; Sevilla Peris, Pablo(Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics), 2015)
[EN] Denote by Ω(n) the number of prime divisors of n ∈ N
(counted with multiplicities). For x ∈ N define the Dirichlet-Bohr radius
P
L(x) to be the best r > 0 such that for every finite Dirichlet polynomial
n≤x
...