Overview
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
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
Bibliographic Information
Book Title: Singular Integrals and Fourier Theory on Lipschitz Boundaries
Authors: Tao Qian, Pengtao Li
DOI: https://doi.org/10.1007/978-981-13-6500-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. and Science Press 2019
Hardcover ISBN: 978-981-13-6499-0Published: 29 March 2019
Softcover ISBN: 978-981-13-6502-7Published: 15 October 2020
eBook ISBN: 978-981-13-6500-3Published: 20 March 2019
Edition Number: 1
Number of Pages: XV, 306
Number of Illustrations: 22 b/w illustrations, 6 illustrations in colour
Topics: Analysis