Abstract
A theory of a class of higher order singular integral under the operator ( L f ) ( u ) = 1 u ¯ 1 [ u 1 ∂ f ∂ u 1 ( u ) - u ¯ 1 ∂ f ∂ u ¯ 1 ( 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.
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