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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 Lp-boundedness of the inner and outer Hilbert transformations for 1<p<∞.
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