Peak-interpolation sets of class C¹

Walter Rudin

Vol. 75 (1978), No. 1, 267–279

DOI: 10.2140/pjm.1978.75.267

Abstract

Let D be a bounded strictly pseudoconvex domain in Cⁿ, with C²-boundary ∂D. Let A(D) be the algebra of all f ∈ C(D) that are holomorphic in D. Let M be a C¹-submanifold of ∂D whose tangent space T_w(M) lies in the maximal complex subspace of T_w(∂D), for every w ∈ M.

The principal result of the present paper is that every compact subset of M is then a peak-interpolation set for A(D).

Mathematical Subject Classification 2000

Primary: 32E25

Secondary: 46J15

Milestones

Received: 6 April 1977

Published: 1 March 1978