The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, and H. Queffélec. "The Bohr inequality for ordinary Dirichlet series." Studia Mathematica 175.3 (2006): 285-304. <http://eudml.org/doc/286147>.

@article{R2006,
abstract = {We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f(s) = ∑_\{n=1\}^\{∞\} aₙn^\{-s\}$ with $||f||_\{∞\} := sup_\{ℜ s>0\} |f(s)| < ∞$, then $∑_\{n=1\}^\{∞\} |aₙ|n^\{-2\} ≤ ||f||_\{∞\}$ and even slightly better, and $∑_\{n=1\}^\{∞\} |aₙ|n^\{-1/2\} ≤ C||f||_\{∞\}$, C being an absolute constant.},
author = {R. Balasubramanian, B. Calado, H. Queffélec},
journal = {Studia Mathematica},
keywords = {Dirichlet series; Bohr radius; Banach spaces of Dirichlet series; hypercontractivity},
language = {eng},
number = {3},
pages = {285-304},
title = {The Bohr inequality for ordinary Dirichlet series},
url = {http://eudml.org/doc/286147},
volume = {175},
year = {2006},
}

TY - JOUR
AU - R. Balasubramanian
AU - B. Calado
AU - H. Queffélec
TI - The Bohr inequality for ordinary Dirichlet series
JO - Studia Mathematica
PY - 2006
VL - 175
IS - 3
SP - 285
EP - 304
AB - We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f(s) = ∑_{n=1}^{∞} aₙn^{-s}$ with $||f||_{∞} := sup_{ℜ s>0} |f(s)| < ∞$, then $∑_{n=1}^{∞} |aₙ|n^{-2} ≤ ||f||_{∞}$ and even slightly better, and $∑_{n=1}^{∞} |aₙ|n^{-1/2} ≤ C||f||_{∞}$, C being an absolute constant.
LA - eng
KW - Dirichlet series; Bohr radius; Banach spaces of Dirichlet series; hypercontractivity
UR - http://eudml.org/doc/286147
ER -