Hilbert Transforms on the Sphere with the Clifford Algebra Setting |
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| Authors: | Tao Qian Yan Yang |
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| Institution: | 1. Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira, S.J., Taipa, Macao, China
2. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, China
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| Abstract: | Through a double-layer potential argument the inner and outer Poisson kernels, the Cauchy-type conjugate inner and outer Poisson
kernels, and the kernels of the Cauchy-type inner and outer Hilbert transformations on the sphere are deduced. We also obtain
Abel sum expansions of the kernels and prove the L
p
-boundedness of the inner and outer Hilbert transformations for 1<p<∞. |
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| Keywords: | |
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