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The Bohr inequality for ordinary Dirichlet series

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Balasubramanian R., Calado B., Queffélec H.

Studia Mathematica

2006

tom 175

nr 3

285-304

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.

Ograniczanie wyników

1 Studia Mathematica

1 Balasubramanian R.

1 Calado B.

1 Queffélec H.

1 2006

Wyniki wyszukiwania

The Bohr inequality for ordinary Dirichlet series