Orlicz Spaces and Generalized Orlicz Spaces
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Resu
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Petteri Harjulehto Peter Hästö
Orlicz Spaces and Generalized Orlicz Spaces
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Editors: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Cambridge Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Petteri Harjulehto • Peter H¨ast¨o
Orlicz Spaces and Generalized Orlicz Spaces
123
Petteri Harjulehto Department of Mathematics and Statistics University of Turku Turku, Finland
Peter H¨ast¨o Department of Mathematics and Statistics University of Turku Turku, Finland
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-15099-0 ISBN 978-3-030-15100-3 (eBook) https://doi.org/10.1007/978-3-030-15100-3 Mathematics Subject Classification (2010): Primary: 46E30; Secondary: 46E35, 42B25, 42B20 © Springer Nature Switzerland AG 2019 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Generalized Orlicz spaces have been an area of growing interest recently. In this book, we present a systematic treatment of these spaces in a general framework. We have tried to make the book accessible to graduate students and a valuable resource for researchers. The manuscript was used in an advanced analysis course at the University of Turku in the fall of 2018, and we thank the participants of the course for their input. We thank our friends and colleagues for their support. We are especially grateful to Ritva Hurri-Syrjänen, Jonne Juusti, Arttu Karppinen, Tetsu Shim
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