A class of singular integrals on the n-complex unit sphere

The operators on the n-complex unit sphere under study have three forms: the singular integrals with holomorphic kernels, the bounded and holomorphic Fourier multipliers, and the Cauchy-Dunford bounded and holomorphic functional calculus of the radial Dirac operator. The equivalence between the three forms and the strong-type (p, p), 1<p<∞, and weak-type (1,1)-boundedness of the operators is proved. The results generalise the work of L. K. Hua, A. Korányli and S. Vagi, W. Rudin and S. Gong on the Cauchy-Szeg(?) kernel and the Cauchy singular integral operator.