A construction of outer functions along curves on the sphere in ℂn

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Abstract

For a simple smooth curv Γe F on the unit sphere in ℂn transverse at all its points, and a non-negative continuous function φ on Γ satisfying ∫Γ log φp ds > - ∞ together with a finite number of necessary compatibility conditions, an holomorphic function f on the unit ball is constructed such that |f|= φ on Γ. The case of a general, not necessarily transverse, curve is also investigated. © 1996 Academic Press, Inc.
Original languageEnglish
Pages (from-to)151-169
JournalJournal of Functional Analysis
Volume140
DOIs
Publication statusPublished - 25 Aug 1996

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