Pacific Journal of Mathematics

Pseudoconvex classes of functions. II. Affine pseudoconvex classes on ${\bf R}^N$.

Zbigniew Slodkowski

Article information

Source
Pacific J. Math., Volume 141, Number 1 (1990), 125-163.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102646777

Mathematical Reviews number (MathSciNet)
MR1028268

Zentralblatt MATH identifier
0693.31007

Subjects
Primary: 32F05
Secondary: 31C10: Pluriharmonic and plurisubharmonic functions [See also 32U05] 32F10: $q$-convexity, $q$-concavity

Citation

Slodkowski, Zbigniew. Pseudoconvex classes of functions. II. Affine pseudoconvex classes on ${\bf R}^N$. Pacific J. Math. 141 (1990), no. 1, 125--163. https://projecteuclid.org/euclid.pjm/1102646777


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References

  • [I] A. D. Alexandrov, Almost everywhere existence of the second differential of a convexfunction and properties of convex surfaces connected with it (in Russian), Leningrad State Univ. Ann. Math. Ser., 6 (1939), 3-35.
  • [2] H. Bremermann, On the conjecture on the equivalenceof the plurisubharmonic functions and Hartogs functions, Math. Ann., 131 (1956),76-86.
  • [3] H. Busemann, Convex Surfaces, Interscience, New York, 1958.
  • [4] R. L. Hunt and J. J. Murray, q-Plurisubharmonicfunctions and generalized Dirichlet problem, Michigan Math. J., 25 (1978),299-316.
  • [5] T. W. Gamelin and N. Sibony, Subharmonicity for uniform algebras,J. Funct. Anal, 35(1980),64-108.
  • [6] J. J. Moreau, Inf convolution,sous-additivite, convexite desfunctions numeriques, J. Math. Pures Appl., 49 (1970), 109-154.
  • [7] Z.Slodkowski, TheBremermann-Dirichlet problemfor q-plurisubharmonicfunc- tions, Ann. Scuola Norm. Sup.-Pisa,Cl. Sci. (4), 11 (1984),303-326.
  • [8] Z.Slodkowski, Local maximum property and q-plurisubharmonicfunctions in uniform algebras,J. Math. Anal. Appl., 115 (1986), 105-130.
  • [9] Z.Slodkowski,Pseudoconvexclassesoffunctions. I.Pseudoconcave andpseudoconvexsets, Pacific J. Math., 134 (1988),343-376.
  • [10] Z.Slodkowski, Complex interpolation ofnormed and quasi-normedspaces in severaldi- mensions I, Trans. Amer. Math. Soc, 308 (1988),685-711.
  • [II] Z.Slodkowski, Pseudoconvex classes of functions. III. Characterization of dual pseudo- convex classes on complex homogeneous spaces, Trans. Amer. Math. Soc, 309 (1988), 165-189.
  • [12] Z.Slodkowski, Approximation of analytic multfunctions, Proc. Amer. Math. Soc, 105 (1989), 387-396.
  • [13] J. B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., 18(1968), 143-148.

See also

  • I : Zbigniew Slodkowski. Pseudoconvex classes of functions. I. Pseudoconcave and pseudoconvex sets. Pacific Journal of Mathematics volume 134, issue 2, (1988), pp. 343-376.
  • Zbigniew Slodkowski. Pseudoconvex classes of functions. {III}. Characterization of dual pseudoconvex classes on complex homogeneous spaces. III [MR 89m:32032] Trans. Amer. Math. Soc. 309 1988 1 165--189.