Advertisement

Complex Analysis and Operator Theory

, Volume 6, Issue 2, pp 447–464 | Cite as

Higher Order Boundary Integral Formula and Integro-Differential Equation on Stein Mainfolds

  • Lüping ChenEmail author
  • Tongde Zhong
  • Tao Qian
Article
  • 75 Downloads

Abstract

This paper deals with the boundary value properties and the higher order singular integro-differential equation. On Stein manifolds, the Hadamard principal value, the Plemelj formula and the composite formula for higher order Bochner–Martinelli type integral are given. As an application, the composite formula is used for discussing the solution of the higher order singular integro-differential equation.

Keywords

Stein manifolds Higher order singular integral Bochner–Martinelli integral Plemelj formula Composite formula Integro-differential equation 

Mathematics Subject Classification (2000)

32A25 32A40 45Exx 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lu Q.K., Zhong T.D.: An extension of the Privalov theorem. Acta Math. Sin. 7, 144–165 (1957) (in Chinese)Google Scholar
  2. 2.
    Zhong T.D.: Integral Representation of Functions of Several Complex Variables and Multidimensional Singular Integral Equations. Xiamen University Press, Xiamen (1986) (in Chinese)Google Scholar
  3. 3.
    Zhong T.D.: Holomorphic Extension on Stein Manifolds. Research Report No. 10, Mittag-Leffler Institute, Stockholm (1987)Google Scholar
  4. 4.
    Qian T., Zhong T.D.: The differential integral equations on smooth closed orientable manifolds. Acta Math. Sci. 21, 1–8 (2001)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chen L.P., Zhong T.D.: Regularization for high order singular integral equations. Integr Equ Oper Theory 62(1), 65–76 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chen L.P., Zhong T.D.: Higher order singular integral equations on complex hypersphere. Acta Math Sci 30B(5), 1785–1792 (2010)MathSciNetGoogle Scholar
  7. 7.
    Henkin G.M., Leiterer J.: Theory of Functions on Complex Manifolds. Akademie-Verlag and Birkhäuser-Verlag, Berlin (1984)zbMATHGoogle Scholar
  8. 8.
    Zhong T.D., Huang S.: Complex Analysis in Several Variables. Hebei Educational Press, Shijiazhuang (1990) (in Chinese)Google Scholar
  9. 9.
    Zhong T.D.: Singular integral equations on Stein manifolds. J. Xiamen Univ. Nat. Sci. 30(3), 231–234 (1991)zbMATHGoogle Scholar
  10. 10.
    Zhong T.D.: Singular Integrals and Integral Representations in Several Complex Variables. Contemporary Mathematics, vol. 142, pp. 151–173. The American Mathematical Society, Providence (1993)Google Scholar
  11. 11.
    Kytmanov A.M.: The Bochner–Martinelli Integral and its Applications. Birkhäuser Verlag, Basel (1995)zbMATHCrossRefGoogle Scholar
  12. 12.
    Hadamard, J.: Lecture on Cauchy’s Problem in Linear Partial Differential Equations. New York (1952)Google Scholar
  13. 13.
    Appell J.M., Kalitvin A.S., Zabrejko P.P.: Partial Integral Operators and Integro-Differential Equations. Marcel Dekker, New York (2000)zbMATHGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China
  2. 2.Faculty of Science and TechnologyThe University of MacauMacauPeople’s Republic of China

Personalised recommendations