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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.

Some translation-invariant Banach function spaces which contain c₀

100%

Lefèvre P., Li D., Queffélec H., Rodríguez-Piazza L.

Studia Mathematica

2004

tom 163

nr 2

137-155

We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c₀.

Ograniczanie wyników

2 Studia Mathematica

2 Queffélec H.

1 Balasubramanian R.

1 Calado B.

1 Lefèvre P.

1 Li D.

1 Rodríguez-Piazza L.

1 2006

1 2004

Wyniki wyszukiwania

The Bohr inequality for ordinary Dirichlet series

Some translation-invariant Banach function spaces which contain c₀