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Singular Integrals and Fourier Theory on Lipschitz Boundaries

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Singular Integrals and Fourier Theory on Lipschitz Boundaries/ by Tao Qian, Pengtao Li.
Author:	Qian, Tao.
other author:	Li, Pengtao.
Description:	XV, 306 p. 28 illus., 6 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-981-13-6500-3
ISBN:	9789811365003

Singular Integrals and Fourier Theory on Lipschitz Boundaries
Qian, Tao.

Singular Integrals and Fourier Theory on Lipschitz Boundaries[electronic resource] /by Tao Qian, Pengtao Li. - 1st ed. 2019. - XV, 306 p. 28 illus., 6 illus. in color.online resource.

Singular integrals and Fourier multipliers on infinite Lipschitz curves -- Singular integral operators on closed Lipschitz curves -- Clifford analysis, Dirac operator and the Fourier transform -- Convolution singular integral operators on Lipschitz surfaces -- Holomorphic Fourier multipliers on infinite Lipschitz surfaces -- Bounded holomorphic Fourier multipliers on closed Lipschitz surfaces -- The fractional Fourier multipliers on Lipschitz curves and surfaces -- Fourier multipliers and singular integrals on Cn.

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. .

ISBN: 9789811365003

Standard No.: 10.1007/978-981-13-6500-3doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Singular Integrals and Fourier Theory on Lipschitz Boundaries
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505 0 $a Singular integrals and Fourier multipliers on infinite Lipschitz curves -- Singular integral operators on closed Lipschitz curves -- Clifford analysis, Dirac operator and the Fourier transform -- Convolution singular integral operators on Lipschitz surfaces -- Holomorphic Fourier multipliers on infinite Lipschitz surfaces -- Bounded holomorphic Fourier multipliers on closed Lipschitz surfaces -- The fractional Fourier multipliers on Lipschitz curves and surfaces -- Fourier multipliers and singular integrals on Cn.
520 $a 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. .
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