The complex Monge-Ampère operator in hyperconvex domains

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1. [Bed] E. Bedford, Survey of pluri-potential theory, Several Complex Variables, Proceedings of the Mittag-Leffler Institute, 1987-1988, J.E. Fornæss (ed.), Princeton Univ. Press, 1993. Zbl0786.31001MR1207855
2. [BT1] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math.37 (1976), 1-44. Zbl0315.31007MR445006
3. [BT2] E. Bedford - B.A. Taylor, A new capacity for plurisubharmonic functions, Acta Math.149 (1982), 1-41. Zbl0547.32012MR674165
4. [Bło1] Z. Blocki, Estimates for the complex Monge-Ampère operator, Bull. Polish Acad. Sci. Math.41 (1993), 151-157. Zbl0795.32003
5. [Bło2] Z. Błocki, On the Lp-stability for the complex Monge-Ampère operator, Michigan Math. J.42(1995), 269-275. Zbl0841.35017
6. [Bło3] Z. Błocki, Smooth exhaustion function in convex domains, to appear in Proc. Amer. Math. Soc. Zbl0889.35030
7. [Ceg] U. Cegrell, Capacities in complex analysis, Aspect of Math. E14, Vieweg, 1988. Zbl0655.32001MR964469
8. [CP] U. Cegrell - L. Persson, The Dirichlet problem for the complex Monge-Ampère operator: Stability in L2, Michigan Math. J.39 (1992), 145-151. Zbl0799.32013MR1137895
9. [CLN] S.S. Chern - H. Levine - L. Nirenberg, Intrinsic norms on a complex manifold, Global Analysis, Univ. of Tokyo Press, 1969, 119-139. Zbl0202.11603MR254877
10. [Dem1] J.-P. Demailly, Mesures de Monge-Ampère et mesures plurisousharmoniques, Math. Z.194 (1987), 519-564. Zbl0595.32006MR881709
11. [Dem2] J.-P. Demailly, Potential theory in several complex variables, preprint, 1989. 
12. [Doo] J.L. Doob, Classical potential theory and its probabilistic counterpart, Grundl. der Math. Wiss.262, Springer-Verlag, 1984. Zbl0549.31001MR731258
13. [Gav] B. Gaveau, Méthodes de contrôle optimal en analyse complexe I. Résolution d'équations de Monge-Ampère, J. Funct. Anal. 25 (1977), 391-411. Zbl0356.35071MR457783
14. [GT] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Grundl. der Math. Wiss. 244, Springer Verlag, 1983. Zbl0562.35001MR737190
15. [Hör] L. Hörmander, An introduction to complex analysis in several variables, North-Holland, 1990. Zbl0685.32001MR1045639
16. [KR] N. Kerzman - J.-P. Rosay, Fonctions plurisousharmoniques d'exhaustion bornées et domaines taut, Math. Ann.257 (1981), 171-184. Zbl0451.32012MR634460
17. [Kli] M. Klimek, Pluripotential theory, Clarendon Press, 1991. Zbl0742.31001MR1150978
18. [Koł] S. Kołodziej, Some sufficient condition for solvability of the Dirichlet problem for the complex Monge-Ampère operator, Ann. Polon. Math.65 (1996), 11-21. Zbl0878.32014
19. [LO] N. Levenberg - M. Okada, On the Dirichlet problem for the complex Monge-Ampère operator, Michigan Math. J.40 (1993), 507-526. Zbl0805.31004MR1236176
20. [RT] J. Rauch - B.A. Taylor, The Dirichlet problem for the multidimensional Monge Ampère equation, Rocky Mountain Math. J.7 (1977), 345-364. Zbl0367.35025MR454331
21. [Rich] R. Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann.175 (1968), 257-286. Zbl0153.15401MR222334
22. [Rud] W. Rudin, Function theory in the unit ball of Cn, Grundl. der Math. Wiss. 241, Springer-Verlag, 1980. Zbl0495.32001MR601594
23. [Sib] N. Sibony, Une classe de domaines pseudoconvexes, Duke Math. J.55 (1987), 299-319. Zbl0622.32016MR894582
24. [Wal] J.B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech.18 (1968), 143-148. Zbl0159.16002MR227465

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