RT Journal Article
T1 Bohr's strip for vector valued Dirichlet series
A1 Defant, Andreas
A1 García, Domingo
A1 Maestre, Manuel
A1 Pérez García, David
AB Bohr showed that the width of the strip (in the complex plane) on which a given Dirichlet series Sigma a(n)/n(s), s is an element of C, converges uniformly but not absolutely, is at most 1/2, and Bohnenblust-Hille that this bound in general is optimal. We prove that for a given infinite dimensional Banach space Y the width of Bohr's strip for a Dirichlet series with coefficients a(n) in Y is bounded by 1 - 1/Cot (Y), where Cot (Y) denotes the optimal cotype of Y. This estimate even turns out to be optimal, and hence leads to a new characterization of cotype in terms of vector valued Dirichlet series.
PB Springer
SN 0025-5831
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50304
UL https://hdl.handle.net/20.500.14352/50304
LA eng
NO MEC and FEDER
DS Docta Complutense
RD 24 ene 2026