H^∞-interpolation from a subset of the boundary

Frank Hayne Beatrous, Jr.

Vol. 106 (1983), No. 1, 23–31

DOI: 10.2140/pjm.1983.106.23

Abstract

We obtain necessary and sufficient conditions for a bounded function on an open subset of the boundary of a smooth, bounded domain D in Cⁿ to be the restriction of a holomorphic function from D into the unit disc. Our condition is a quadratic inequality involving the Szegő kernel of D which is the boundary analogue of the classical Pick-Nevanlinna condition for interpolation in the unit disc.

Mathematical Subject Classification 2000

Primary: 32A35

Secondary: 47B35

Milestones

Received: 15 September 1981

Published: 1 May 1983