Sur un théorème de Mooney relatif aux fonctions analytiques bornées

Eric Amar

Vol. 49 (1973), No. 2, 311–314

DOI: 10.2140/pjm.1973.49.311

Abstract

We give a short proof of the following theorem of Mooney: If {Φ_n} is a sequence in L¹(−π,π) such that lim_n ∫ fΦ_n = l(f) exists for all f ∈ H^∞, then there is Φ ∈ L¹ such that l(f) = ∫ fΦ for all f ∈ H^∞.

Mathematical Subject Classification 2000

Primary: 46E15

Secondary: 30A78

Milestones

Received: 13 September 1972

Published: 1 December 1973