Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-03T21:38:12.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Transformation formula of higher order integrals

Part of: Higher-dimensional theory Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 April 2009

Tao Qian  and
Tongde Zhong
Tao Qian
Affiliation:
School of Mathematics and Computer Sciences The University of New EnglandArmidale, NSW 2351 Australia e-mail:tao@mcs.une.edu.au
Tongde Zhong
Affiliation:
Institute of Mathematics Xiamen University Xiamen 361005 P. R., China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By using integration by parts and Stokes' formula the authors give a new definition of the Hadamard principal value of higher order singular integrals on the complex hypersphere in Cn. Then the transformation formula for the higher order singular integrals is deduced.

Keywords

complex hyperspherehigher order singular integraltransformation formula.

MSC classification

Secondary: 32A25: Integral representations; canonical kernels (Szegő, Bergman, etc.) 31B10: Integral representations, integral operators, integral equations methods
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 155 - 164
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Fox, C., ‘A generalization of the Cauchy principal value’, Canad. J. Math. 9 (1957), 110–117.CrossRefGoogle Scholar
[2]Gong, S., Integrals of Cauchy type on the ball (International Press, Cambridge MA, 1993).Google Scholar
[3]Hadamard, J., Lectures on Cauchy's problem in linear partial differential equations (Dover, New York, 1953).Google Scholar
[4]Muskhelishvili, N. I., Singular integral equations (Noordhoff, Groningen, 1953).Google Scholar
[5]Wang, C. Y., ‘Hadamard's principal value of the singular integral’, Chinese Ann. Math. 3 (2) (1982), 195–202.Google Scholar
[6]Wang, X. Q., Singular integrals and analyticity theorems in several complex variables (Ph. D. Thesis, Uppsala University, Sweden, 1990).Google Scholar
[7]Zhong, T. D., Integral representation of functions of several complex variables and multidimensional singular integral equations (Xiamen University Press, Xiamen, 1986) (Chinese).Google Scholar