Singular Integrals and Fourier Theory on Lipschitz Boundaries
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Beschreibung
The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s. The subject of singular integrals and the related Fourier multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis and partial differential equations. The book elaborates on the basic framework, the Fourier methodology, and the main results in various contexts, especially addressing the following topics: singular integral operators with holomorphic kernels, fractional integral and differential operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high-dimensional Fueter mapping theorem with applications. The book offers a valuable resource for all graduate students and researchers interested in singular integrals and Fourier multipliers.
The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s. The subject of singular integrals and the related Fourier multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis and partial differential equations. The book elaborates on the basic framework, the Fourier methodology, and the main results in various contexts, especially addressing the following topics: singular integral operators with holomorphic kernels, fractional integral and differential operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high-dimensional Fueter mapping theorem with applications. The book offers a valuable resource for all graduate students and researchers interested in singular integrals and Fourier multipliers.
States systemically the theory of singular integrals and Fourier multipliers on the Lipschitz graphs and surfaces Elaborates the basic framework, essential thoughts and main results Reveals the equivalence between the operator algebra of the singular integrals, Fourier multiplier Operators and the Cauchy-Dunford functional calculus of the Dirac operators
Autor*in
Tao Qian
Themen in »Singular Integrals and Fourier Theory on Lipschitz Boundaries«
Singular integrals Fourier multipliers Lipschitz curves Clifford analysis Fourier transform Lipschitz surface Holomorphic Fourier multipliers
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“The main audience for this book would be those interested in the importance of Fourier multipliers in Harmonic Analysis. … this book would serve as a nice reference on recent developments on singular integrals and Fourier multipliers on various Lipschitz surfaces.” (Eric Stachura, MAA Reviews, December 22, 2019)
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