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© 2019

Singular Integrals and Fourier Theory on Lipschitz Boundaries

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Table of contents

About this book

Introduction

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. 

Keywords

Singular integrals Fourier multipliers Lipschitz curves Clifford analysis Fourier transform Lipschitz surface Holomorphic Fourier multipliers

Authors and affiliations

  1. 1.Macau Institute of Systems EngineeringMacau University of Science and TechnologyMacaoChina
  2. 2.School of Mathematics and StatisticsQingdao UniversityQingdaoChina

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
  • Copyright Information Springer Nature Singapore Pte Ltd. and Science Press 2019
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-981-13-6499-0
  • Softcover ISBN 978-981-13-6502-7
  • eBook ISBN 978-981-13-6500-3
  • Edition Number 1
  • Number of Pages XV, 306
  • Number of Illustrations 22 b/w illustrations, 6 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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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)