Foundations of Symmetric Spaces of Measurable Functions Lorentz, Mar
Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results
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Ben-Zion A. Rubshtein Genady Ya. Grabarnik Mustafa A. Muratov Yulia S. Pashkova
Foundations of Symmetric Spaces of Measurable Functions Lorentz, Marcinkiewicz and Orlicz Spaces
Developments in Mathematics VOLUME 45 Series Editors: Krishnaswami Alladi, University of Florida, Gainesville, FL, USA Hershel M. Farkas, Hebrew University of Jerusalem, Jerusalem, Israel
More information about this series at http://www.springer.com/series/5834
Ben-Zion A. Rubshtein • Genady Ya. Grabarnik Mustafa A. Muratov • Yulia S. Pashkova
Foundations of Symmetric Spaces of Measurable Functions Lorentz, Marcinkiewicz and Orlicz Spaces
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Ben-Zion A. Rubshtein Mathematics Ben Gurion University of the Negev Be’er Sheva, Israel
Genady Ya. Grabarnik Mathematics and Computer Science St. John’s University New York, NY, USA
Mustafa A. Muratov Mathematics and Computer Sciences V.I. Vernadsky Crimean Federal University Simferopol, Russian Federation
Yulia S. Pashkova Mathematics and Computer Sciences V.I. Vernadsky Crimean Federal University Simferopol, Russian Federation
ISSN 1389-2177 ISSN 2197-795X (electronic) Developments in Mathematics ISBN 978-3-319-42756-0 ISBN 978-3-319-42758-4 (eBook) DOI 10.1007/978-3-319-42758-4 Library of Congress Control Number: 2016953731 Mathematics Subject Classification (2010): 46E30, 46E35, 26D10, 26D15, 46B70, 46B42, 46B10, 47G10 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, 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 publisher, 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 publisher 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Inna, Tanya, Andrey Fany, Yaacob, Laura, Golda Ajshe, Elvira, Enver, Lenur Anna, Ludmila, Sergey
Foreword
This book is the first part of the textbook Symmetric Spaces of Measurable Functions. It contains the main definitions and results of the theory of symmetric (rearrangement invariant) spaces. Special a
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