Arkiv för Matematik

  • Ark. Mat.
  • Volume 39, Number 1 (2001), 181-200.

Jensen measures and boundary values of plurisubharmonic functions

Frank Wikström

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Abstract

We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions in B-regular domain. This theorem implies that the two classes of Jensen measures coincide in B-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.

The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function.

Article information

Source
Ark. Mat., Volume 39, Number 1 (2001), 181-200.

Dates
Received: 10 March 1999
Revised: 21 October 1999
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898716

Digital Object Identifier
doi:10.1007/BF02388798

Mathematical Reviews number (MathSciNet)
MR1821089

Zentralblatt MATH identifier
1021.32014

Rights
2001 © Institut Mittag-Leffler

Citation

Wikström, Frank. Jensen measures and boundary values of plurisubharmonic functions. Ark. Mat. 39 (2001), no. 1, 181--200. doi:10.1007/BF02388798. https://projecteuclid.org/euclid.afm/1485898716


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References

  • Błocki, Z., The complex Monge-Ampère operator in hyperconvex domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23 (1996), 721–747.
  • Carlehed, M., Cegrell, U. and Wikström, F., Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function, Ann. Polon. Math. 71 (1999), 87–103.
  • Cegrell, U., Capacities in Complex Analysis, Vieweg, Braunschweig, 1988.
  • Cegrell, U., Approximation of plurisubharmonic functions and integration by parts, Preprint, 1998.
  • Demailly, J.-P., Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z. 194 (1987), 519–564.
  • Edwards, D. A., Choquet boundary theory for certain spaces of lower semicontinuous functions, in Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) (Birtel, F., ed.), pp. 300–309, Scott-Foresman, Chicago, Ill., 1966.
  • Fornæss, J. E. and Narasimhan, R., The Levi problem on complex spaces with singularities, Math. Ann. 248 (1980), 47–72.
  • Fornæss, J. E. and Stensønes, B., Lectures on Counterexamples in Several Complex Variables, Princeton Univ. Press, Princeton, N. J., 1987.
  • Lárusson, F. and Sigurdsson, R., Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998), 1–39.
  • Poletsky, E. A., Plurisubharmonic functions as solutions of variational problems, in Several Complex Variables and Complex Geometry, Part 1 (Santa Cruz, Calif., 1989) (Bedford, E., D'Angelo, J. P., Greene, R. E. and Krantz, S. G., (eds.), pp. 163–171. Amer. Math. Soc., Providence, R. I., 1991.
  • Poletsky, E. A., Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85–144.
  • Sibony, N., Une classe de domaines pseudoconvexes, Duke Math. J. 55 (1987), 299–319.
  • Walsh, J. B., Continuity of envelopes of plurisubharmonic functions, J. Math. Mech. 18 (1968/1969), 143–148.