Zeros of H^p functions in several complex variables

Nicholas Th. Varopoulos

Vol. 88 (1980), No. 1, 189–246

DOI: 10.2140/pjm.1980.88.189

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 = f⁻¹(0) for some f ∈ H^p(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