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| Singular Integrals in Several Complex Variables (II)------HadamardPrincipal Value on a Sphere |
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Citation： |
Shi Jihuai,Gong Sheng.Singular Integrals in Several Complex Variables (II)------HadamardPrincipal Value on a Sphere[J].Chinese Annals of Mathematics B,1983,4(3):307~318 |
| Page view： 915
Net amount： 590 |
Authors： |
Shi Jihuai; Gong Sheng |
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| Abstract： |
Hadamard introduced the concept of finite parts of divergent integrals, i.e. Hadamard principal value, when he researched the Cauchy problems of the hyperbolic type partial differential equations. In this paper,the authors try to generalize this concept to the singular integrals on a sphere of several complex variables space Cn. The Hadamard: principal value of higher order singular integral
$\[\frac{1}{{{\omega _{2n - 1}}}}\int_{u\bar u'} {\frac{{f(u)\dot u}}{{{{(1 - v\bar u')}^{n + 1/2}}}}} \]$
is defined and the corresponding Plemelj formula is obtained. |
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