Gaussian Capacity Analysis
This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequ
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Liguang Liu Jie Xiao Dachun Yang Wen Yuan
Gaussian Capacity Analysis
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York AnnaWienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Liguang Liu • Jie Xiao • Dachun Yang • Wen Yuan
Gaussian Capacity Analysis
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Liguang Liu School of Mathematics Renmin University of China Beijing, China Dachun Yang Laboratory of Mathematics and Complex Systems (Ministry of Education of China) School of Mathematical Sciences Beijing Normal University Beijing, China
Jie Xiao Department Mathematics & Statistics Memorial University St. John’s, Newfoundland and Labrador Canada Wen Yuan Laboratory of Mathematics and Complex Systems (Ministry of Education of China) School of Mathematical Sciences Beijing Normal University Beijing, China
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-95039-6 ISBN 978-3-319-95040-2 (eBook) https://doi.org/10.1007/978-3-319-95040-2 Library of Congress Control Number: 2018951056 Mathematics Subject Classification: 31B15, 31B35, 42B35, 52A38, 53A07, 53C65, 60D05 © Springer Nature Switzerland AG 2018 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 This monograph Gaussian Capacity Analysis documents the functional p-capacity and its extreme BV -capacity in Gauss space with applications to tracing the Gaussian Sobolev p-space and its extreme BV -space as well as the indu
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