The Bremermann-Dirichlet problem for q-plurisubharmonic functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 11 (1984) no. 2, pp. 303-326. 
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     title = {The {Bremermann-Dirichlet} problem for $q$-plurisubharmonic functions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {303--326},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 11},
     number = {2},
     year = {1984},
     mrnumber = {764948},
     zbl = {0583.32046},
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     url = {http://archive.numdam.org/item/ASNSP_1984_4_11_2_303_0/}
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Slodkowski, Zbigniew. The Bremermann-Dirichlet problem for $q$-plurisubharmonic functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 11 (1984) no. 2, pp. 303-326. http://archive.numdam.org/item/ASNSP_1984_4_11_2_303_0/

[1] A.D. Alexandrov, Almost everywhere existence of the second differential of a convex function and properties of convex surfaces connected with it (in Russian), Lenningrad State Univ. Ann. Math. Ser. 6 (1939), pp. 3-35.

[2] R. Basener, Boundaries for product algebras (Preprint).

[3] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampere equation, Inventiones Math., 37 (1976), pp. 1-44. | MR | Zbl

[4] H. Bremermann, On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Shilov boundaries, Trans. Amer. Math. Soc., 91 (1976), pp. 246-276. | MR | Zbl

[5] H. Buseman, Convex surfaces, Interscience, New York, 1958. | MR | Zbl

[6] N. Dunford - J.T. Schwartz, Linear operators, Part II, Spectral Theory, Interscience publishers, New York, 1963. | MR | Zbl

[7] R.C. Gunning - H. Rossi, Analytic functions of several complex variables, Prentice-Hall Inc., Englewood Cliffs, 1965. | MR | Zbl

[8] R.L. Hunt - J.J. Murray, q-Plurisubharmonic functions and a generalized Dirichlet problem, Mich. Math. Journ., 25 (1978), pp. 299-316. | MR | Zbl

[9] M. Kalka, On a conjecture of Hunt and Murray concerning q-plurisubharmonic functions, Proc. Amer. Math. Soc., 73 (1979), pp. 30-34. | MR | Zbl

[10] R.T. Rockafellar, Convex analysis, Princeton University Press, Princeton, N. J., 1970. | MR | Zbl

[11] C.A. Rogers, Hausdorff measures, Cambridge University Press, 1970. | MR | Zbl

[12] Z. Slodkowski, Analytic multifunctions, pseudoconvex domains and uniform algebras. Talk at Conference on Banach Algebras and Several Complex Variables, Yale University, June, 1983. | Zbl

[13] Z. Slodkowski, Local maximum properties and q-plurisubharmonic functions in uniform algebras, submitted for publication.

[14] J.B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., 18 (1968), pp. 143-148. | MR | Zbl