Singular Integrals and Fourier Theory on Lipschitz Boundaries
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 integral
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Singular Integrals and Fourier Theory on Lipschitz Boundaries
Singular Integrals and Fourier Theory on Lipschitz Boundaries
Tao Qian Pengtao Li •
Singular Integrals and Fourier Theory on Lipschitz Boundaries
123
Tao Qian Macau Institute of Systems Engineering Macau University of Science and Technology Macao, China
Pengtao Li School of Mathematics and Statistics Qingdao University Qingdao, Shandong, China
ISBN 978-981-13-6499-0 ISBN 978-981-13-6500-3 https://doi.org/10.1007/978-981-13-6500-3
(eBook)
Jointly published with Science Press, Beijing, China The print edition is not for sale in China Mainland. Customers from China Mainland please order the print book from: Science Press. Library of Congress Control Number: 2019931519 © Springer Nature Singapore Pte Ltd. and Science Press 2019 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
This book is a sincere dedication to Professor Alan McIntosh
Preface
From the idea to the content, this book is basically Alan McIntosh’s theory. In this book, we state systemically the theory of singular integrals and Fourier multipliers on Lipschitz graphs and surfaces which stems largely from the famous “CoifmanMcIntosh-Meyer Theorem” since 1980s. The book elaborates the basic framework, essential thoughts, and main results of the theory. At the same time, this book also serves as a comprehensive reference on recent developments of this topic. The subject of Fourier multipliers on Lipschitz surfaces has a profound background in harmonic analysis and partial differential equations. When we study boundary value problems of second-order elliptic operators, we need to deal with L2-boundedness of the Cauchy-type integral op
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