Bourgain algebras on the unit disk

Joseph A. Cima, Karel M. Stroethoff and Keith Yale

Vol. 160 (1993), No. 1, 27–41

DOI: 10.2140/pjm.1993.160.27

Abstract

The Bourgain algebra of H^∞(𝔻) relative to L^∞(𝔻) is shown to be H^∞(𝔻) + C(𝔻) + V , where V is an ideal of functions in L^∞(𝔻) which vanish in an appropriate sense near the boundary of 𝔻.

Mathematical Subject Classification 2000

Primary: 46J10

Secondary: 46J30, 47B35

Milestones

Received: 15 February 1991

Revised: 20 April 1992

Published: 1 September 1993