Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary
Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 1085-1100

Voir la notice de l'article provenant de la source Cambridge University Press

We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.
DOI : 10.4153/CJM-2000-045-x
Mots-clés : 32F07, 32F05
Xing, Yang. Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary. Canadian journal of mathematics, Tome 52 (2000) no. 5, pp. 1085-1100. doi: 10.4153/CJM-2000-045-x
@article{10_4153_CJM_2000_045_x,
     author = {Xing, Yang},
     title = {Complex {Monge-Amp\`ere} {Measures} of {Plurisubharmonic} {Functions} with {Bounded} {Values} {Near} the {Boundary}},
     journal = {Canadian journal of mathematics},
     pages = {1085--1100},
     year = {2000},
     volume = {52},
     number = {5},
     doi = {10.4153/CJM-2000-045-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-045-x/}
}
TY  - JOUR
AU  - Xing, Yang
TI  - Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary
JO  - Canadian journal of mathematics
PY  - 2000
SP  - 1085
EP  - 1100
VL  - 52
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-045-x/
DO  - 10.4153/CJM-2000-045-x
ID  - 10_4153_CJM_2000_045_x
ER  - 
%0 Journal Article
%A Xing, Yang
%T Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary
%J Canadian journal of mathematics
%D 2000
%P 1085-1100
%V 52
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-045-x/
%R 10.4153/CJM-2000-045-x
%F 10_4153_CJM_2000_045_x

[B] [B] Bedford, E., Survey of pluri-potential theory. Several Complex Variables: Proceedings of theMittag-Leffler Inst. 1987–1988, (ed. John Erik Fornaess), Math. Notes 38, Princeton Univ. Press, 1993. Google Scholar

[B-T1] [B-T1] Bedford, E. and Taylor, B. A., The Dirichlet problem for the complexMonge-Ampère operator. Invent.Math. 37(1976), 1–44. Google Scholar

[B-T2] [B-T2] Bedford, E. and Taylor, B. A., A new capacity for plurisubharmonic functions. Acta Math. 149(1982), 1–40. Google Scholar

[B-T3] [B-T3] Bedford, E. and Taylor, B. A., Fine topology, Šilov boundary and (ddc)n. J. Funct. Anal. 72(1987), 225–251. Google Scholar

[B-T4] [B-T4] Bedford, E. and Taylor, B. A., Plurisubharmonic functions with logarithmic singularities. Ann. Inst. Fourier (Grenoble) (4) 38(1988), 133–171. Google Scholar

[C1] [C1] Cegrell, U., Sums of continuous plurisubharmonic functions and the complex Monge–Ampère operator. Math. Z. 193(1986), 373–380. Google Scholar

[C2] [C2] Cegrell, U., Pluricomplex energy. ActaMath. 180(1998), 187–217. Google Scholar

[C-P] [C-P] Cegrell, U. and Persson, L., The Dirichlet problem for the complex Monge-Ampère operator: stability in L2. Michigan Math. J. 39(1992), 145–151. Google Scholar

[D] [D] Demailly, J.-P., Monge-Ampère operators, Lelong numbers and intersection theory. In: Complex Analysis and Geometry, Univ. Ser. Math., Plenum, New York, 1993, 115–193. Google Scholar

[K] [K] Kiselman, C. O., Sur la definition de l’opérateur deMonge-Ampère complexe. Analyse Complexe: Proceedings, Toulouse (1983), 139–150, Lecture Notes in Math. 1094, Springer-Verleg. Google Scholar

[KO1] [KO1] Kolodziej, S., The range of the complex Monge-Ampère operator, II. Indiana Univ.Math. J. 44(1995), 765–782. Google Scholar

[KO2] [KO2] Kolodziej, S., The range of the complex Monge-Ampère operator. Indiana Univ.Math. J. 43(1994), 1321–1338. Google Scholar

[KO3] [KO3] Kolodziej, S., Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator. Ann. Polon. Math. 65(1996), 11–21. Google Scholar

[KO4] [KO4] Kolodziej, S., The complex Monge-Ampère equation. ActaMath. 180(1998), 69–117. Google Scholar

[P] [P] Persson, L., On the Dirichlet problem for the complex Monge-Ampère operator. Thesis, Ume°a, 1992. Google Scholar

[S] [S] Sibony, N., Quelques problémes de prolongement de courants en analyse complexe. DukeMath. J. 52(1985), 157–197. Google Scholar

[X] [X] Xing, Y., Continuity of the complex Monge-Ampère operator. Proc. Amer.Math. Soc. 124(1996), 457–467. Google Scholar

Cité par Sources :