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Esterlè's proof of the tauberian theorem for Beurling algebras

H. G. Dales, W. K. Hayman (1981)

Annales de l'institut Fourier

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for L 1 ( R ) using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras L φ 1 ( R ) . Our estimates need a theorem of Hayman and Korenblum.

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