Vol. 43, No. 2, 1972

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A theorem on bounded analytic functions

Michael Cannon Mooney

Vol. 43 (1972), No. 2, 457–463
Abstract

The purpose of this paper is to prove the following

Theorem: Let ϕ12, be an infinite sequence of functions in L1([0,2π]) such that L(f) = limn→∞ 02πf(ei𝜃)ϕn(𝜃)d𝜃 exists for every f H. Then there is a ϕ L1([0,2π]) such that L(f) = 02πf(ei𝜃)ϕ(𝜃)d𝜃 for all f H.

Mathematical Subject Classification 2000
Primary: 46J15
Secondary: 30A98
Milestones
Received: 15 April 1971
Revised: 3 February 1972
Published: 1 November 1972
Authors
Michael Cannon Mooney