L^p and H^p extensions of holomorphic functions from subvarieties of analytic polyhedra

Kenzō Adachi, Mats Andersson and Hong Rae Cho

Vol. 189 (1999), No. 2, 201–210

DOI: 10.2140/pjm.1999.189.201

Abstract

Let V be a regular subvariety of a non-degenerate analytic polyhedron Ω ⊂ ℂⁿ. If V intersects ∂Ω transversally in a certain sense, then each bounded holomorphic function on V has a bounded holomorphic extension to Ω. Furthermore, a function in H^p(V ) has an extension in H^p(Ω). Under a weaker transversality condition each f ∈𝒪(V ) ∩ L^p(V ) has an extension to a function in 𝒪(Ω) ∩ L^p(Ω), p < ∞.

Milestones

Received: 5 August 1997

Published: 1 June 1999