Vol. 88, No. 1, 1980

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ISSN: 0030-8730
Zeros of Hp functions in several complex variables

Nicholas Th. Varopoulos

Vol. 88 (1980), No. 1, 189–246
Abstract

Let Ω be a strictly pseudoconvex smoothly bounded domain in Cn and let M Ω be a complex hypersurface in Ω. In this paper I develop a condition that is sufficient to ensure that M = f1(0) for some f Hp(Ω) (i.e., some f belonging to some Hardy class of Ω). That condition refers to the growth of the 2n 2 dimensional volume of M as it approaches the boundary Ω.

Mathematical Subject Classification 2000
Primary: 32A35
Milestones
Received: 9 November 1978
Published: 1 May 1980
Authors
Nicholas Th. Varopoulos