Optimal Domain And Integral Extension Of Operators: Acting In Function Spaces (operator Theory: Advances And Applications)

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This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Applications are given to Maurey-Rosenthal factorization of operators and to classical operators arising in commutative harmonic analysis. The main tool is the vector measure associated to such an operator, which produces a corresponding space of integrable functions and an integration operator.

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Operator Theory: Advances and Applications Vol. 180 Editor: I. Gohberg (GLWRULDO2I½FH School of Mathematical Sciences Tel Aviv University Ramat Aviv, Israel Editorial Board: D. Alpay (Beer-Sheva) J. Arazy (Haifa) A. Atzmon (Tel Aviv) J. A. Ball (Blacksburg) A. Ben-Artzi (Tel Aviv) H. Bercovici (Bloomington) A. Böttcher (Chemnitz) K. Clancey (Athens, USA) L. A. Coburn (Buffalo) R. E. Curto (Iowa City) K. R. Davidson (Waterloo, Ontario) R. G. Douglas (College Station) A. Dijksma (Groningen) H. Dym (Rehovot) P. A. Fuhrmann (Beer Sheva) B. Gramsch (Mainz) J. W. Helton (La Jolla) M. A. Kaashoek (Amsterdam) H. G. Kaper (Argonne) S. T. Kuroda (Tokyo) P. Lancaster (Calgary) L. E. Lerer (Haifa) B. Mityagin (Columbus) V. Olshevsky (Storrs) M. Putinar (Santa Barbara) L. Rodman (Williamsburg) J. Rovnyak (Charlottesville) D. E. Sarason (Berkeley) I. M. Spitkovsky (Williamsburg) S. Treil (Providence) H. Upmeier (Marburg) S. M. Verduyn Lunel (Leiden) D. Voiculescu (Berkeley) D. Xia (Nashville) D. Yafaev (Rennes) Honorary and Advisory Editorial Board: C. Foias (Bloomington) T. Kailath (Stanford) H. Langer (Vienna) P. D. Lax (New York) H. Widom (Santa Cruz) Optimal Domain and Integral Extension of Operators Acting in Function Spaces Susumu Okada Werner J. Ricker Enrique A. Sánchez Pérez Birkhäuser Basel · Boston · Berlin Authors: Susumu Okada Centre for Mathematics and its Applications $XVWUDOLDQ1DWLRQDO8QLYHUVLW\  &DQEHUUD$&7   Australia e-mail: [email protected] Werner J. Ricker Mathematisch-Geographische Fakultät Katholische Universität Eichstätt-Ingolstadt (LFKVWlWW *HUPDQ\ e-mail: [email protected] Enrique A. Sánchez Pérez Instituto de Matemática Pura y Aplicada Universidad Politécnica de Valencia Camino de Vera s/n 9DOHQFLD Spain e-mail: [email protected] 0DWKHPDWLFDO6XEMHFW&ODVVL½FDWLRQ%&$$$( *%%% /LEUDU\RI&RQJUHVV&RQWURO1XPEHU Bibliographic information published by Die Deutsche Bibliothek. 'LH'HXWVFKH%LEOLRWKHNOLVWVWKLVSXEOLFDWLRQLQWKH'HXWVFKH1DWLRQDOELEOLRJUD½H detailed bibliographic data is available in the Internet at http://dnb.ddb.de ,6%1%LUNKlXVHU9HUODJ$*%DVHO- Boston - Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of WKHPDWHULDOLVFRQFHUQHGVSHFL½FDOO\WKHULJKWVRIWUDQVODWLRQUHSULQWLQJUHXVHRI LOOXVWUDWLRQVUHFLWDWLRQEURDGFDVWLQJUHSURGXFWLRQRQPLFUR½OPVRULQRWKHUZD\VDQG storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin 32%R[&+%DVHO6ZLW]HUODQG Part of Springer Science+Business Media Printed on acid-free paper produced from
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