TY - JOUR

T1 - Esterlè's proof of the tauberian theorem for Beurling algebras

AU - Dales, H.G.

AU - Hayman, W. K.

PY - 1981

Y1 - 1981

N2 - Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^1({\bf R})$ 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 $L^1_\varphi ({\bf R})$. Our estimates need a theorem of Hayman and Korenblum.

AB - Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^1({\bf R})$ 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 $L^1_\varphi ({\bf R})$. Our estimates need a theorem of Hayman and Korenblum.

U2 - 10.5802/aif.852

DO - 10.5802/aif.852

M3 - Journal article

VL - 31

SP - 141

EP - 150

JO - Annales de L'Institut Fourier

JF - Annales de L'Institut Fourier

SN - 1777-5310

IS - 4

ER -