Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂn

Mark L. Agranovsky

doi:10.1007/s11854-011-0008-9

Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂⁿ

Mark L. Agranovsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let f ∈ C^ω(∂Bⁿ), where Bⁿ is the unit ball of ℂⁿ. We prove that if a,b ∈ B̄ⁿ, a ≠ b, for every complex line L passing through one of a or b, the restricted function f{pipe}L∩∂Bⁿ has a holomorphic extention to the cross-section L∩Bⁿ, then f is the boundary value of a holomorphic function in Bⁿ.

Original language	English
Pages (from-to)	293-304
Number of pages	12
Journal	Journal d'Analyse Mathematique
Volume	113
Issue number	1
DOIs	https://doi.org/10.1007/s11854-011-0008-9
State	Published - Jan 2011

Bibliographical note

Funding Information:
∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.

Funding

∗This work was partially supported by the grant from ISF (Israel Science Foundation) 688/08. Some of this research was done as a part of European Science Foundation Networking Program HCAA.

Funders	Funder number
Israel Science Foundation	688/08

Access to Document

10.1007/s11854-011-0008-9

Cite this

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