Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces A Sharp Theory
Systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives atomic, molecul
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Ryan Alvarado Marius Mitrea
Hardy Spaces on AhlforsRegular Quasi Metric Spaces A Sharp Theory
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and NY Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Ryan Alvarado • Marius Mitrea
Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces A Sharp Theory
123
Marius Mitrea Department of Mathematics University of Missouri Columbia, MO, USA
Ryan Alvarado Department of Mathematics University of Missouri Columbia, MO, USA
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-18131-8 DOI 10.1007/978-3-319-18132-5
ISSN 1617-9692
(electronic)
ISBN 978-3-319-18132-5
(eBook)
Library of Congress Control Number: 2015940436 Mathematics Subject Classification (2010): 42B30, 42B35, 42B20, 42B25, 28C15, 35J25, 43A85, 54E35, 54E50, 46A16, 46F05 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
By systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces (H p spaces) in the setting of d-dimensional Alhlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part debuts by revisiting a number of basic analytical tools in quasi-metric space analysis, for which new versions are produced in the nature of best possible. These results, themselves of independent interest, include a sharp Lebesgue differentiation theorem, a maximally smooth approximation to the id
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