The Bremermann-Dirichlet problem for q -plurisubharmonic functions

Zbigniew Slodkowski

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1984)

  • Volume: 11, Issue: 2, page 303-326
  • ISSN: 0391-173X

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Slodkowski, Zbigniew. "The Bremermann-Dirichlet problem for $q$-plurisubharmonic functions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 11.2 (1984): 303-326. <http://eudml.org/doc/83933>.

@article{Slodkowski1984,
author = {Slodkowski, Zbigniew},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {q-plurisubharmonic functions; Dirichlet problem; p-plurisubharmonic functions},
language = {eng},
number = {2},
pages = {303-326},
publisher = {Scuola normale superiore},
title = {The Bremermann-Dirichlet problem for $q$-plurisubharmonic functions},
url = {http://eudml.org/doc/83933},
volume = {11},
year = {1984},
}

TY - JOUR
AU - Slodkowski, Zbigniew
TI - The Bremermann-Dirichlet problem for $q$-plurisubharmonic functions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1984
PB - Scuola normale superiore
VL - 11
IS - 2
SP - 303
EP - 326
LA - eng
KW - q-plurisubharmonic functions; Dirichlet problem; p-plurisubharmonic functions
UR - http://eudml.org/doc/83933
ER -

References

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  1. [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. [2] R. Basener, Boundaries for product algebras (Preprint). 
  3. [3] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampere equation, Inventiones Math., 37 (1976), pp. 1-44. Zbl0315.31007MR445006
  4. [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. Zbl0091.07501MR136766
  5. [5] H. Buseman, Convex surfaces, Interscience, New York, 1958. Zbl0196.55101MR105155
  6. [6] N. Dunford - J.T. Schwartz, Linear operators, Part II, Spectral Theory, Interscience publishers, New York, 1963. Zbl0128.34803MR1009163
  7. [7] R.C. Gunning - H. Rossi, Analytic functions of several complex variables, Prentice-Hall Inc., Englewood Cliffs, 1965. Zbl0141.08601MR180696
  8. [8] R.L. Hunt - J.J. Murray, q-Plurisubharmonic functions and a generalized Dirichlet problem, Mich. Math. Journ., 25 (1978), pp. 299-316. Zbl0378.32013MR512901
  9. [9] M. Kalka, On a conjecture of Hunt and Murray concerning q-plurisubharmonic functions, Proc. Amer. Math. Soc., 73 (1979), pp. 30-34. Zbl0413.35023MR512052
  10. [10] R.T. Rockafellar, Convex analysis, Princeton University Press, Princeton, N. J., 1970. Zbl0193.18401MR274683
  11. [11] C.A. Rogers, Hausdorff measures, Cambridge University Press, 1970. Zbl0204.37601MR281862
  12. [12] Z. Slodkowski, Analytic multifunctions, pseudoconvex domains and uniform algebras. Talk at Conference on Banach Algebras and Several Complex Variables, Yale University, June, 1983. Zbl0587.32031
  13. [13] Z. Slodkowski, Local maximum properties and q-plurisubharmonic functions in uniform algebras, submitted for publication. 
  14. [14] J.B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., 18 (1968), pp. 143-148. Zbl0159.16002MR227465

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