On the multiplicative Cousin problems for N^p(D)

K. Adachi

Vol. 80 (1979), No. 2, 297–303

DOI: 10.2140/pjm.1979.80.297

Abstract

Let D be a strictly convex domain in Cⁿ with C²-class boundary. Let N^p(D), 1 < p < ∞, be the set of all holomorphic functions f in D such that (log ⁺|f|)^p has a harmonic majorant. The purpose of this paper is to show that the multiplicative Cousin problems for N^p(D), 1 < p < ∞, are solvable.

Mathematical Subject Classification 2000

Primary: 32E05

Milestones

Received: 28 October 1977

Revised: 19 June 1978

Published: 1 February 1979