Removable singularities for \(H^ p\)-functions. (English) Zbl 0532.32004
Authors’ abstract: Given a domain D in \({\mathbb{C}}^ n\), a holomorphic function f on D is said to belong to \(H^ p(D)\), \(0<p<\infty\), provided that \(| f|^ p\) admits a harmonic majorant in D. In this note it is shown that \(H^ p(D\backslash E)=H^ p(D)\) whenever E is a relative closed polar subset of D.
Reviewer: E.Bedford
MSC:
32D20 | Removable singularities in several complex variables |
32D15 | Continuation of analytic objects in several complex variables |
32A35 | \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables |
32F99 | Geometric convexity in several complex variables |
32C05 | Real-analytic manifolds, real-analytic spaces |