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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Communicated by Hans G. Feichtinger.
The work was supported by research grant of the University of Macau No. RG079/04-05S/QT/FST.
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Qian, T., Yang, Y. Hilbert Transforms on the Sphere with the Clifford Algebra Setting. J Fourier Anal Appl 15, 753–774 (2009). https://doi.org/10.1007/s00041-009-9062-4
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DOI: https://doi.org/10.1007/s00041-009-9062-4
Keywords
- Poisson kernel
- Conjugate Poisson kernel
- Schwarz kernel
- Hilbert transformation
- Cauchy singular integral
- Double-layer potential
- Clifford analysis