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Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations
Tao Qian
2001-02
Source PublicationAdvances in Applied Clifford Algebras
ISSN0188-7009
Volume11Pages:53–76
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.

KeywordFourier Multiplier Singular Integral Dirac Operator The Unit Sphere In Rn Lipschitz Domains
DOIhttps://doi.org/10.1007/BF03042209
Language英語English
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Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorTao Qian
AffiliationFaculty of Science and Technology,The University of Macau,Macao (via Hong Kong)
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
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Tao Qian. Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations[J]. Advances in Applied Clifford Algebras,2001,11:53–76.
APA Tao Qian.(2001).Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations.Advances in Applied Clifford Algebras,11,53–76.
MLA Tao Qian."Singular integrals and Fourier multipliers on unit spheres and their Lipschitz perturbations".Advances in Applied Clifford Algebras 11(2001):53–76.
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