Acta mathematica scientia, Series B >
HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE
Received date: 2006-02-25
Revised date: 2009-01-04
Online published: 2010-09-20
Supported by
The project was supported by the Natural Science Foundation of Fujian Province of China (S0850029, 2008J0206), Innovation Foundation of Xiamen University (XDKJCX20063019), and the National Science Foundation of China (10771174).
A theory of a class of higher order singular integral under the operator (Lf)(u)=1/u1[u1 ∂f}/ ∂u1 (u)-u1 ∂f/ ∂u1 (u)+f(u)] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
CHEN Lv-Ping , ZHONG Tong-De . HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1785 -1792 . DOI: 10.1016/S0252-9602(10)60172-5
[1] Hadamard J. Lecture on Cauchy's Problem in Linear Partial Differential Equations. New York: Dover Publications, 1952
[2] Gong S. Integrals of Cauchy Type on the Ball. New York: International Press Co, 1993
[3] Wang X Q. Singular integrals and analyticity theorems in several complex variables
[D]. Sweden: Uppsala University, 1990
[4] Qian T, Zhong T D. Transformation formula of higher order integrals. J Austral Math Soc (Seris A), 2000, 68: 155--164
[5] Appell J M, Kalitvin A S, Zabrejko P P. Partial Integral Operators and Integro-Differential Equations. New York: Marcel Dekker, Inc, 2000
[6] Mikhlin S G. Integral Equations and Its Applications. Shanghai: Commercial Press, 1957 (in Chinese)
[7] Zhong T D, Chen L P. The permutation formula of singular integrals with Bochner-Martinelli kernel on stein manifolds. Acta Mathematica Scientia, 2006, 26B(4): 679--690
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