Arkiv för Matematik

  • Ark. Mat.
  • Volume 28, Number 1-2 (1990), 221-230.

Traces of pluriharmonic functions on curves

Bo Berndtsson and Joaquim Bruna

Full-text: Open access

Abstract

We prove that, if γ is a simple smooth curve in the unit sphere in Cn, the space o pluriharmonic functions in the unit ball, continuous up to the boundary, has a trace of finite cof dimension in the space of all continuous functions on the curve.

Note

First author partially supported by the Swedish Natural Science Research Council. Second author partially supported by CICYT grant PB85-0374.

Article information

Source
Ark. Mat., Volume 28, Number 1-2 (1990), 221-230.

Dates
Received: 2 May 1989
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898014

Digital Object Identifier
doi:10.1007/BF02387377

Mathematical Reviews number (MathSciNet)
MR1084012

Zentralblatt MATH identifier
0727.31005

Rights
1990 © Institut Mittag-Leffler

Citation

Berndtsson, Bo; Bruna, Joaquim. Traces of pluriharmonic functions on curves. Ark. Mat. 28 (1990), no. 1-2, 221--230. doi:10.1007/BF02387377. https://projecteuclid.org/euclid.afm/1485898014


Export citation

References

  • Bruna, J. and Ortega, J. M., Interpolation by holomorphic functions smooth to the boundary in the unit ball of Cn, Math. Ann. 274 (1986), 527–575.
  • Burns, D. and Stout, E. L., Extending functions from submanifolds of the boundary, Duke Math. J. 43 (1976), 391–404.
  • Chirka, E. M. and Khenkin, G. M., Boundary properties of holomorphic functions of several variables (Russian), Sovremennye problemy matematiki (Ed. Gamkrelidze, R. V.)4, 13–142, Itogi nauki i tekhniki, VINITI, Moscow, 1975 (English translation: J. Soviet Math. 5 (1976), 612–687.)
  • Forstnerič, F., Regularity of varieties in strictly pseudoconvex domains, Publications Matemàtiques 32 (1988), 145–150.
  • Nagel, A., Smooth zero-sets and interpolation sets for some algebras of holomorphic functions on strictly pseudoconvex domains, Duke Math. J. 43 (1976), 323–348.
  • Nagel, A., Cauchy transforms of measures and a characterization of smooth peak interpolation sets for the ball algebra, Rocky Mountain J. Math. 9 (1979), 299–305.
  • Rosay, J.-P., A remark on a theorem by F. Forstnerič, Ark. Mat. 28 (1990), 311–314.
  • Rosay, J.-P. and Stout, E. L., On pluriharmonic interpolation, preprint.
  • Rudin, W., Peak-interpolation sets of class C1, Pacific. J. Math. 75 (1978), 267–279.
  • Rudin, W., Function theory in the unit ball of Cn, Springer-Verlag, New York, Heidelberg, Berlin, 1980.