The Bohr inequality for ordinary Dirichlet series

• Autorzy: R. Balasubramanian , B. Calado , H. Queffélec
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A45: Multipliers
• 30B10: Power series (including lacunary series)
• 11M41: Other Dirichlet series and zeta functions
• 30B50: Dirichlet series and other series expansions, exponential series
• 40A05: Convergence and divergence of series and sequences
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 175
• Numer: 3
• Strony: 285-304

Daty

wydano

2006

Twórcy

autor

R. Balasubramanian

• The Institute of Mathematical Sciences, Chennai 600 113, India

autor

B. Calado

• Laboratoire de Mathématiques, Centre d'Orsay, Université Paris-Sud XI, Bâtiment 425, 91405 Orsay, France

autor

H. Queffélec

• UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/sm175-3-7