Titlebook: Singular Integrals and Fourier Theory on Lipschitz Boundaries; Tao Qian,Pengtao Li Book 2019 Springer Nature Singapore Pte Ltd. and Scienc

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Clifford Analysis, Dirac Operator and the Fourier Transform, to establish the theory of convolution singular integrals and Fourier multipliers on Lipschitz surfaces. In Sect. ., we give a brief survey on basics of Clifford analysis. In Sect. ., we state the monogenic functions on sectors introduced by Li, McIntosh, Qian [.]. Section . is devoted to the Fouri

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Convolution Singular Integral Operators on Lipschitz Surfaces,rators on the Lipschitz surfaces . is a meaningful question. The increase of the dimensions means that we need to apply a new method to solve the above question. In 1994, C. Li, A. McIntosh and S. Semmes embedded . into Clifford algebra . and considered the class of holomorphic functions on the sect

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Holomorphic Fourier Multipliers on Infinite Lipschitz Surfaces,perators on the Euclidean spaces .. Because Plancherel’s identity involving the Fourier transform is invalid on Lipschitz surfaces ., the relation between singular Cauchy integral operators and Fourier multipliers on . is an open problem for a long time. In 1994, by the aid of Clifford analysis, Li,

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Bounded Holomorphic Fourier Multipliers on Closed Lipschitz Surfaces, integrals and Fourier multipliers for the case of starlike Lipschitz curves on the complex plane. The cases of .tours and their Lipschitz disturbance are studied in [., .]. In 1998 and 2001, by a generalization of Fueter’s theorem, T. Qian established the theory of bounded holomorphic Fourier multi

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The Fractional Fourier Multipliers on Lipschitz Curves and Surfaces,ecent years, see the author’s paper joint with Leong [.] and the joint work [.]. In the above chapters, we state the convolution singular integral operators and the related bounded holomorphic Fourier multipliers on the finite and infinite Lipschitz curves and surfaces. Let . and . be the regions de

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Book 2019itz 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 frame

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