Pacific Journal of Mathematics

Pseudoconvex classes of functions. I. Pseudoconcave and pseudoconvex sets.

Zbigniew Slodkowski

Article information

Source
Pacific J. Math., Volume 134, Number 2 (1988), 343-376.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102689266

Mathematical Reviews number (MathSciNet)
MR961240

Zentralblatt MATH identifier
0693.31006

Subjects
Primary: 32F05
Secondary: 31C05: Harmonic, subharmonic, superharmonic functions 31C10: Pluriharmonic and plurisubharmonic functions [See also 32U05] 32F10: $q$-convexity, $q$-concavity

Citation

Slodkowski, Zbigniew. Pseudoconvex classes of functions. I. Pseudoconcave and pseudoconvex sets. Pacific J. Math. 134 (1988), no. 2, 343--376. https://projecteuclid.org/euclid.pjm/1102689266


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References

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  • [2] R. Coifman, A theory of complex interpolation for families of Banach Spaces, Adv. in Math., 33 (1982), 203-229.
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  • [4] R. L. Hunt and J. J. Murray, q-Plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J., 25 (1978), 299-316.
  • [5] S. G. Krantz, Function Theory of Several Complex Variables,John Wiley and Sons, New York 1982.
  • [6] T. Ransford, Interpolation and extrapolation of analytic multivalued functions, Proc. London Math. Soc, (3) 50 (1985), 480-504.
  • [7] C. E. Rickart, Natural Function Algebras, Universitext, Springer-Verlag, Berlin- Heidelberg-New York 1979.
  • [8] Z. Slodkowski, The Bremermann-Dirichlet problemfor q-plurisubharmonicfunc- tions, Ann. Scuola Norm. Sup. (Pisa), Ser. IV, vol. XI (1984), 303-326.
  • [9] Z. Slodkowski, Local maximum property and q-plurisubharmonicfunctions in uniform algebras,J. Math. Anal. AppL, 115 (1986), 105-130.
  • [10] Z. Slodkowski, Complex interpolation families of normed spaces overseveral-dimen- sional parameter space, Abstract of the Special Session in Several Complex Variables, 826th Meeting of the A.M.S., Indianapolis, April 1986.
  • [11] Z. Slodkowski, Pseudoconvex classes offunctions, II.
  • [12] Z. Slodkowski, Pseudoconvex classes of functions, III., Trans. Amer. Math. Soc, (to appear).
  • [13] Z. Slodkowski, Complex interpolation of normed and quasi-normed spaces in several dimensions, I. Trans Amer. Math. Soc, (to appear).
  • [14] Z. Slodkowski, Pseudoconvex classesoffunctions, IV.
  • [15] J. Wermer, Maximum modulus algebras and singularity sets, Proc. Roy. Soc Edinburgh. Sect. A, 86 (1980), 327-331.
  • [16] M. Wu, On certain Kahler manifolds which are q-complete, Proc Symp. in Pure Math., 41 (1984), 253-276.

See also

  • II : Zbigniew Slodkowski. Pseudoconvex classes of functions. II. Affine pseudoconvex classes on ${\bf R}^N$. Pacific Journal of Mathematics volume 141, issue 1, (1990), pp. 125-163.
  • 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.