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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.