Jensen measures and unbounded B - regular domains in C n

Quang Dieu Nguyen[1]; Dau Hoang Hung[2]

  • [1] University of Education (Dai Hoc Su Pham Hanoi) Department of Mathematics 136 Xuan Thuy, Cau Giay Hanoi (Vietnam) Current address: Seaoul National Universiy Department of Mathematics 151-742 Seoul (Korea)
  • [2] Vinh University Department of Mathematics Vinh (Vietnam)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 4, page 1383-1406
  • ISSN: 0373-0956

Abstract

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Following Sibony, we say that a bounded domain Ω in C n is B -regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in C n . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

How to cite

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Nguyen, Quang Dieu, and Hung, Dau Hoang. "Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$." Annales de l’institut Fourier 58.4 (2008): 1383-1406. <http://eudml.org/doc/10352>.

@article{Nguyen2008,
abstract = {Following Sibony, we say that a bounded domain $\Omega $ in $C^n$ is $B$-regular if every continuous real valued function on the boundary of $\Omega $ can be extended continuously to a plurisubharmonic function on $\Omega $. The aim of this paper is to study an analogue of this concept in the category of unbounded domains in $C^n$. The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work},
affiliation = {University of Education (Dai Hoc Su Pham Hanoi) Department of Mathematics 136 Xuan Thuy, Cau Giay Hanoi (Vietnam) Current address: Seaoul National Universiy Department of Mathematics 151-742 Seoul (Korea); Vinh University Department of Mathematics Vinh (Vietnam)},
author = {Nguyen, Quang Dieu, Hung, Dau Hoang},
journal = {Annales de l’institut Fourier},
keywords = {Plurisubharmonic function; Dirichlet-Bremermann problem; $B$-regular domain; plurisubharmonic function; -regular domain},
language = {eng},
number = {4},
pages = {1383-1406},
publisher = {Association des Annales de l’institut Fourier},
title = {Jensen measures and unbounded $B-$regular domains in $\{\mathbf\{C\}\}^n$},
url = {http://eudml.org/doc/10352},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Nguyen, Quang Dieu
AU - Hung, Dau Hoang
TI - Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 4
SP - 1383
EP - 1406
AB - Following Sibony, we say that a bounded domain $\Omega $ in $C^n$ is $B$-regular if every continuous real valued function on the boundary of $\Omega $ can be extended continuously to a plurisubharmonic function on $\Omega $. The aim of this paper is to study an analogue of this concept in the category of unbounded domains in $C^n$. The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work
LA - eng
KW - Plurisubharmonic function; Dirichlet-Bremermann problem; $B$-regular domain; plurisubharmonic function; -regular domain
UR - http://eudml.org/doc/10352
ER -

References

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  1. E. Bedford, A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40 Zbl0547.32012MR674165
  2. Z. Blocki, The complex Monge-Ampère operator in hyperconvex domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23 (1996), 721-747 Zbl0878.31003MR1469572
  3. H. Bremermann, On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Silov boundaries, Trans. Amer. Math. Soc. 91 (1959), 246-276 Zbl0091.07501MR136766
  4. A. Brown, C. Pearcy, An Introduction to Analysis, 154 (1995), Springer-Verlag Zbl0820.00003MR1320708
  5. D. Edwars, Choquet boundary theory for certain spaces of lower semicontinuous functions, Function algebras (1966), 300-309, Scott-Foresman, Chicago Zbl0145.38601MR196521
  6. J. Fornaess, J. Wiegerinck, Approximation of plurisubharmonic functions, Ark. Mat. 27 (1989), 257-272 Zbl0693.32009MR1022280
  7. K. W. K. Hayman, B. Kennedy, Subharmonic function, London Mathematical Society Monographs, I (1976), Academic Press, Harcourt Brace Jovanovich, London-New York Zbl0419.31001
  8. Maciej Klimek, Pluripotential theory, 6 (1991), The Clarendon Press Oxford University Press, New York Zbl0742.31001MR1150978
  9. Q. D. Nguyen, Approximation of plurisubharmonic functions on bounded domains in C n , Michigan Math. J. 54 (2006), 697-711 Zbl1155.32021MR2280502
  10. Q. D. Nguyen, N. T. Dung, D. H. Hung, B - regularity of certain domains in C n ,, Annales Polon. Math. 86 (2005), 137-152 Zbl1088.32007MR2181017
  11. Q. D. Nguyen, F. Wikström, Jensen measures and approximation of plurisubharmonic functions, Michigan Math. J. 53 (2005), 529-544 Zbl1102.31009MR2207205
  12. W. Rudin, Real and Complex Analysis, (1966), McGraw-Hill Book Co., New York-Toronto, Ont.-London Zbl0142.01701MR210528
  13. N. Shcherbina, G. Tomassini, The Dirichlet problem for Levi-flat graphs over unbounded domains, Internat. Math. Res. Notices 3 (1999), 111-151 Zbl0935.32027MR1672246
  14. N. Sibony, Une classe des domaines pseudoconvex, Duke Math. J. 55 (1987), 299-319 Zbl0622.32016MR894582
  15. A. Simioniuc, G. Tomassini, The Bremermann-Dirichlet problem for unbounded domains in C n  Zbl1144.32019
  16. J. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech. 18 (1968/1969), 143-148 Zbl0159.16002MR227465
  17. J. Wikström, Jensen measures and boundary values of plurisubharmonic functions, Ark. Mat. 39 (2001), 181-200 Zbl1021.32014MR1821089

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