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Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations

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Abstract

A theory of singular integrals with monogenic kernels on star-shaped Lipschitz surfaces inR n is established. The class of singular integrals forms an operator algebra identical to the class of bounded holomorphic Fourier multipliers, as well as to the Cauchy-Dunford bounded holomorphic functional calculus of the spherical Dirac operator. The study proposes a new method inducing Clifford holomorphic functions from holomorphic functions of one complex variable, by means of which the study on the sphere is reduced to that on the unit circle.

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  1. Faculty of Science and Technology, The University of Macau, P.O. Box 3001, Macao (via Hong Kong)

    Tao Qian

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Qian, T. Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations. AACA 11 (Suppl 1), 53–76 (2001). https://doi.org/10.1007/BF03042209

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