Peak points in boundaries not of finite type

Alan Noell

Vol. 123 (1986), No. 2, 385–390

DOI: 10.2140/pjm.1986.123.385

Abstract

It is known that, in domains in C² which are pseudoconvex and of finite type, compact subsets of peak sets for A^∞(D) are peak sets for A^∞(D). We give an example of a convex domain D (not of finite type) whose weakly pseudoconvex boundary points form a line segment K, with the property: K is a peak set for A^∞(D), but a point p ∈ K is not a peak point for any A^α(D), α > 0. We also consider briefly the case when the weakly pseudoconvex boundary points form a disc.

Mathematical Subject Classification 2000

Primary: 32E25

Secondary: 32A40, 32E35, 46J20

Milestones

Received: 18 July 1983

Revised: 20 December 1984

Published: 1 June 1986