Hostname: page-component-54dcc4c588-hp6zs Total loading time: 0 Render date: 2025-09-11T21:30:37.639Z Has data issue: false hasContentIssue false
  • English
  • Français

On holomorphic extensions from spheres in ℂ2

Published online by Cambridge University Press:  14 November 2011

Josip Globevnik
Josip Globevnik
Affiliation:
Institute of Mathematics, Physics and Mechanics, E.K. University of Ljubljana, Ljubljana, Yugoslavia
Get access Rights & Permissions [Opens in a new window]

Synopsis

A theorem of Rudin states that if B is the open unit ball in ℂN, N > 1, if 0<ρ < 1, if is the family of all complex lines in ℂN at a distance ρ from the origin and if f ∈ C(∂B) is such that for every Λ∈ the function f|Λ∂B has a continuous extension to Λ ∩ B which is holomorphic in Λ ∩ B, then f has a continuous extension to B which is holomorphic in B. In this paper we show that when N = 2, the theorem still holds if is replaced by a considerably smaller family.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 113 - 120
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Bochner, S. and Martin, W. T.. Several complex variables (Princeton University Press, 1948).Google Scholar
2Globevnik, J.. On boundary values of holoraorphic functions on balls. Proc. Amer. Math. Soc. 85 (1982), 61–64.CrossRefGoogle Scholar
3Nagel, A. and Rudin, W.. Moebius-invariant function spaces on balls and spheres. Duke Math. J. 43 (1976), 841–865.CrossRefGoogle Scholar
4Rudin, W.. Function theory in the unit ball of ℂn. Grundl. Math. Wiss. 241 (Springer, Berlin: 1980).Google Scholar
5Rudin, W.. Function theory in polydiscs (New York: Benjamin, 1969).Google Scholar