The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian; B. Calado; H. Queffélec

R. Balasubramanian ; B. Calado ; H. Queffélec

Studia Mathematica, Tome 173 (2006), p. 285-304 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $f (s) = \sum_{n = 1}^{\infty} a ₙ n^{- s}$ with ${| | f | |}_{\infty} : = s u p_{ℜ s > 0} | f (s) | < \infty$ , then $\sum_{n = 1}^{\infty} | a ₙ | n^{- 2} {\leq | | f | |}_{\infty}$ and even slightly better, and $\sum_{n = 1}^{\infty} | a ₙ | n^{- 1 / 2} {\leq C | | f | |}_{\infty}$ , C being an absolute constant.

Publié le : 2006-01-01

Zbl 1110.30001

EUDML-ID : urn:eudml:doc:286147

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R. Balasubramanian; B. Calado; H. Queffélec. The Bohr inequality for ordinary Dirichlet series. Studia Mathematica, Tome 173 (2006) pp. 285-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-3-7/