Following Sibony, we say that a bounded domain in is -regular if every continuous real valued function on the boundary of can be extended continuously to a plurisubharmonic function on . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work
En suivant Sibony, nous dirons qu’un domaine borne de est régulier si toute fonction continue à valeurs réelles sur la frontière de peut être prolongée continûment à une fonction plurisousharmonique sur . Le but de ce papier est d’étudier une notion analogue dans la catégorie des domaines non bornés dans . L’usage des mesures de Jensen relatives à des classes de fonctions plurisousharmoniques jouent un rôle clé dans notre travail.
Keywords: Plurisubharmonic function, Dirichlet-Bremermann problem, $B$-regular domain
Mot clés : fonction plurisousharmonique, Dirichlet-Bremermann problème, domaine $B$-régulier
Nguyen, Quang Dieu 1, 2; Hung, Dau Hoang 3
@article{AIF_2008__58_4_1383_0, author = {Nguyen, Quang Dieu and Hung, Dau Hoang}, title = {Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$}, journal = {Annales de l'Institut Fourier}, pages = {1383--1406}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {4}, year = {2008}, doi = {10.5802/aif.2388}, mrnumber = {2427964}, zbl = {1156.32020}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2388/} }
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 SP - 1383 EP - 1406 VL - 58 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2388/ DO - 10.5802/aif.2388 LA - en ID - AIF_2008__58_4_1383_0 ER -
%0 Journal Article %A Nguyen, Quang Dieu %A Hung, Dau Hoang %T Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$ %J Annales de l'Institut Fourier %D 2008 %P 1383-1406 %V 58 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2388/ %R 10.5802/aif.2388 %G en %F AIF_2008__58_4_1383_0
Nguyen, Quang Dieu; Hung, Dau Hoang. Jensen measures and unbounded $B-$regular domains in ${\mathbf{C}}^n$. Annales de l'Institut Fourier, Volume 58 (2008) no. 4, pp. 1383-1406. doi : 10.5802/aif.2388. https://aif.centre-mersenne.org/articles/10.5802/aif.2388/
[1] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982), pp. 1-40 | DOI | MR | Zbl
[2] The complex Monge-Ampère operator in hyperconvex domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 23 (1996), pp. 721-747 | Numdam | MR | Zbl
[3] On a generalized Dirichlet problem for plurisubharmonic functions and pseudo-convex domains. Characterization of Silov boundaries, Trans. Amer. Math. Soc., Volume 91 (1959), pp. 246-276 | MR | Zbl
[4] An Introduction to Analysis, Graduate Texts in Mathematics, 154, Springer-Verlag, 1995 | MR | Zbl
[5] Choquet boundary theory for certain spaces of lower semicontinuous functions, Function algebras (1966), pp. 300-309 | MR | Zbl
[6] Approximation of plurisubharmonic functions, Ark. Mat., Volume 27 (1989), pp. 257-272 | DOI | MR | Zbl
[7] Subharmonic function, London Mathematical Society Monographs, I, Academic Press, Harcourt Brace Jovanovich, London-New York, 1976 no. 9, pp. xvii+284 | Zbl
[8] Pluripotential theory, London Mathematical Society Monographs. New Series, 6, The Clarendon Press Oxford University Press, New York, 1991 (Oxford Science Publications) | MR | Zbl
[9] Approximation of plurisubharmonic functions on bounded domains in , Michigan Math. J., Volume 54 (2006) no. 3, pp. 697-711 | DOI | MR | Zbl
[10] regularity of certain domains in ,, Annales Polon. Math., Volume 86 (2005) no. 2, pp. 137-152 | DOI | MR | Zbl
[11] Jensen measures and approximation of plurisubharmonic functions, Michigan Math. J., Volume 53 (2005), pp. 529-544 | DOI | MR | Zbl
[12] Real and Complex Analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966 | MR | Zbl
[13] The Dirichlet problem for Levi-flat graphs over unbounded domains, Internat. Math. Res. Notices, Volume 3 (1999), pp. 111-151 | DOI | MR | Zbl
[14] Une classe des domaines pseudoconvex, Duke Math. J., Volume 55 (1987), pp. 299-319 | DOI | MR | Zbl
[15] The Bremermann-Dirichlet problem for unbounded domains in (http://it.arxiv.org/math/pdf/0702/0702179v1.pdf, preprint, 2007, to be published in Manuscripta Mat)
[16] Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., Volume 18 (1968/1969), pp. 143-148 | MR | Zbl
[17] Jensen measures and boundary values of plurisubharmonic functions, Ark. Mat., Volume 39 (2001), pp. 181-200 | DOI | MR | Zbl
Cited by Sources: