A problem of Douglas and Rudin on factorization

Jean Bourgain

Vol. 121 (1986), No. 1, 47–50

DOI: 10.2140/pjm.1986.121.47

Abstract

If f is a bounded measurable function on the circle π, then ∫ _πlog |f|dm > −∞ expresses the necessary and sufficient condition on f≠0 to be of the form f = g ⋅h where g,h ∈ H^∞. This question was proposed by Douglas and Rudin in [1], where they approximate unimodular functions on π by quotients of Blaschke products.

Mathematical Subject Classification 2000

Primary: 30D55

Secondary: 42A50, 46J15

Milestones

Received: 10 April 1984

Revised: 12 September 1984

Published: 1 January 1986