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

摘要

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