Hilbert transforms on the sphere and Lipschitz surfaces
Qian T.
Conference Name6th Congress of the International-Society-for-Analysis-Its-Applications-and-Computation
Source PublicationTrends in Mathematics
Conference DateAUG 13-18, 2007
Conference PlaceMiddle East Tech Univ, Ankara, TURKEY

Through a double-layer potential argument we define harmonic conjugates of the Cauchy type and prove their existence and uniqueness in Lipschitz domains. We further define inner and outer Hilbert transformations on Lipschitz surfaces and prove their boundedness in L, where the range for the index p depends on the Lipschitz constant of the boundary surface. The inner and outer Poisson kernels, the Cauchy type conjugate inner and outer Poisson kernels, and the kernels of the inner and outer Hilbert transformations on the sphere are obtained. We also obtain Abel sum expansions of the kernels. The study serves as a justification of the methods in a series of papers of Brackx et al. based on their method for computation of a certain type of harmonic conjugates.

KeywordCauchy Integral Clifford Algebra Conjugate Poisson Kernel Double-layer Potential Hilbert Transformation Poisson Kernel Schwarz Kernel
URLView the original
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000264751300016
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeConference paper
CollectionUniversity of Macau
AffiliationUniversidade de Macau
Recommended Citation
GB/T 7714
Qian T.. Hilbert transforms on the sphere and Lipschitz surfaces[C],2009:259-275.
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