$q$-plurisubharmonicity and $q$-pseudoconvexity in $\mathbf{C}^n$

@inproceedings{Diu2006qplurisubharmonicityA,
  title={\$q\$-plurisubharmonicity and \$q\$-pseudoconvexity in \$\mathbf\{C\}^n\$},
  author={Nguyễn Quang Diệu},
  year={2006}
}
We generalize classical results for plurisubharmonic functions and hyperconvex domain to $q$-plurisubharmonic functions and $q$-hyperconvex domains. We show, among other things, that $B_q$-regular domains are $q$-hyperconvex. Moreover, some smoothing results for $q$-plurisubharmonic functions are also given. 

References

Publications referenced by this paper.
SHOWING 1-9 OF 9 REFERENCES

Pluripotential theory”, London Mathematical Society Monographs

M. Klimek
  • New Series
  • 1991

Hörmander, “An introduction to complex analysis in several variables

L. Hö
  • Third edition, North-Holland Mathematical Library
  • 1990

Fornæss, Smoothing q-convex functions and vanishing theorems, Invent. Math

J.E.K. Diederich
  • 1985

Rosay, Fonctions plurisousharmoniques d’exhaustion

N. Kerzman, J.-P
  • bornées et domaines taut, Math. Ann
  • 1981

Grauert, Théorème de finitude pour la cohomologie des espaces complexes

H. AG A. Andreotti
  • Bull. Soc. Math. France
  • 1962