SpringerLink
Log in

q-subharmonicity and q-convex domains in ℂn

  • Regular paper
  • Published:
Mathematica Slovaca

Abstract

In this paper we study q-subharmonic and q-plurisubharmonic functions in ℂn. Next as an application, we give the notion of q-convex domains in ℂn which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. AHN, H.— DIEU, N. Q.: The Donnelly-Fefferman theorem on q-pseudoconvex domains, Osaka J. Math. 46 (2009), 599–610.

    MATH  MathSciNet  Google Scholar 

  2. ANDREOTTI, A.— GRAUERT, H.: Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. Frace. 90 (1962), 193–259.

    MATH  MathSciNet  Google Scholar 

  3. CHEN, S. C.— SHAW, M. C.: Partial Differential Equations in Several Complex Variables. AMS/IP Stud. Adv. Math. 19, Amer. Math. Soc., Providence, RI, 2001.

    MATH  Google Scholar 

  4. COLTOIU, M.— MIHALACHE, N.: Pseudoconvex domains on complex spaces with singularities, Compositio Math. 72 (1989), 241–247.

    MATH  MathSciNet  Google Scholar 

  5. DEMAILLY, J. P.: Complex Analytic and Differential Geometry. Prerint, 2007.

    Google Scholar 

  6. DIEU, N. Q.: q-plurisubharmonicity and q-pseudoconvexity in ℂn, Publ. Mat. 50 (2006), 349–369.

    Article  MATH  MathSciNet  Google Scholar 

  7. GREENE, R. E.— WU, H. H.: Embedding of open riemannian manifolds by harmonic functions, Ann. Inst. Fourier (Grenoble) 25 (1975), 215–235.

    Article  MATH  MathSciNet  Google Scholar 

  8. GUNNING, R. C.— ROSSI, H.: Analytic Functions of Several Complex Variables, Prentice-Hall, Inc, Englewood Cliffs, NJ, 1965.

    MATH  Google Scholar 

  9. HAI, L. M.— HONG, N. X.: Weighted estimates for solutions of the \(\bar \partial\) -equation in q-pseudoconvex domains, Vietnam J. Math. 38 (2010), 211–225.

    MATH  MathSciNet  Google Scholar 

  10. HO, L. H.: \(\bar \partial\) -problem on weakly q-convex domains, Math. Ann. 290 (1991), 3–18.

    Article  MATH  MathSciNet  Google Scholar 

  11. HÖRMANDER, L.: An introduction to complex analysis in several variables. North-Holland Math. Library 7, North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  12. KEZMAN, N.— ROSAY, J. P.: Fonctions plurisubharmoniques d’exhaustion bornées et domains taut, Mat. Ann. 257 (1981), 171–184.

    Article  Google Scholar 

  13. HUNT, L. R.— MURRAY, J. J.: q-plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J. 25 (1978), 171–184.

    MathSciNet  Google Scholar 

  14. SLODKOWSKI, Z.: The Bremermann-Dirichlet problem for q-plurisubharmonic functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), 303–326.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education (Dai hoc Su Pham Ha Noi), 136 Xuan Thuy Street Caugiay District, Ha Noi, Viet Nam

    Nguyen Van Khue, Le Mau Hai & Nguyen Xuan Hong

Authors
  1. Nguyen Van Khue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Le Mau Hai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nguyen Xuan Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Le Mau Hai.

Additional information

Communicated by Ján Borsík

About this article

Cite this article

Van Khue, N., Hai, L.M. & Hong, N.X. q-subharmonicity and q-convex domains in ℂn . Math. Slovaca 63, 1247–1268 (2013). https://doi.org/10.2478/s12175-013-0169-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s12175-013-0169-3

2010 Mathematics Subject Classification

Keywords

Search

Navigation