Editorial Boar d James Humphreys (Chair) David Saltman David Sattinger Ronald Stern ANALISIS DE FOURIER by Javier Duoandikoetxea Zuazo Published in Spanish by Addison-Wesley and Universidad Autonoma de Madrid in 1995 Translated from the Spanish by David Cruz-Uribe, SFO 2000 Mathematics Subject Classification. Primary 42B15, 42B20, 42B25. ABSTRACT. The purpose of this book is to develop Fourier analysis using the real variable methods introduced by A. P. Calderon and A. Zygmund. It begins by reviewing the theory of Fourier series and integrals, and introduces the Hardy-Littlewood maximal function. It then treats the Hilbert transform and its higher dimensional analogues, singular integrals. In subsequent chapters it discusses some more recent topics: H1 and BMO, weighted norm inequalities, Littlewood-Paley theory, and the T l theorem. At the end of each chapter are extensive references and notes on additional results. Library of Congress Cataloging-in-Publication Data Duoandikoetxea, Zuazo, Javier. [Analisis de Fourier. English] Fourier analysis / Javier Duoandikoetxea translated and revised by David Cruz-Uribe. p. cm. (Graduate studies in mathematics v. 29) Includes bibliographical references and index. ISBN 0-8218-2172-5 1. Fourier analysis. I. Title. II. Series. QA403.5.D8313 2000 515'.2433—dc21 00-064301 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permissionOams.org. © 2001 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ 10 9 8 7 6 5 4 3 2 14 13 12 11 10 09
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