TY - JOUR
T1 - A construction of outer functions along curves on the sphere in ℂn
AU - Bruna, Joaquim
PY - 1996/8/25
Y1 - 1996/8/25
N2 - 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.
AB - 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.
U2 - https://doi.org/10.1006/jfan.1996.0103
DO - https://doi.org/10.1006/jfan.1996.0103
M3 - Article
VL - 140
SP - 151
EP - 169
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
ER -