Function Spaces and Applications Proceedings of the US-Swedish Semin
This seminar is a loose continuation of two previous conferences held in Lund (1982, 1983), mainly devoted to interpolation spaces, which resulted in the publication of the Lecture Notes in Mathematics Vol. 1070. This explains the bias towards that subjec
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1302 M. Cwikel J. Peetre Y. Sagher H. Wallin (Eds.)
Function Spaces and Applications Proceedings of the US- Swedish Seminar held in Lund, Sweden, June 15-21, 1986
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Department of Mathematics Haifa 32000, Israel Jaak Peetre Lund Institute of Technology, Department of Mathematics S-221 00 Lund, Sweden Yoram Sagher University of Illinois at Chicago Circle, Department of Mathematics Chicago, IL 60680, USA HansWallin University of Umeă, Department of Mathematics S-901 87 Umeă., Sweden
Mathematics Subject Classification (1980): 41A25, 46E30, 46E35, 47835 ISBN 978-3-540-18905-3 DOI 10.1007/978-3-540-38841-8
ISBN 978-3-540-38841-8 (eBook)
This work is subject to copyright. Ali rights are reserved, whether the whole or pari of the material is concerned, specifically the rights of translation, reprinting, re-usa of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or paris thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in ils version of June 24, 1985, and a copyright fee must always be paid. Violations fali under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1988
2148/3140-54321 o
Foreword These are the proceedings of a seminar held in Lund in June 1986, devoted to function space methods in analysis. The organizers felt that recent developments in Interpolation Theory have important implications in various areas of analysis, and that further work in Interpolation would benefit from the input of new problems and applications. Thus the makeup of the seminar was considerably broader than its two predecessors (Lund 1982 and 1983}. It is particularly appropriate that these seminars have taken place in Lund, where lnterpolation Theory was horn some 60 years ago. To further emphasize the historical origin of the subject, the collection is preceded by a historical Jecture on the life of Marcel Riesz. The organizers wish to thank Naturvetenskapliga Forskningsrădet and the N.S.F. for supporting the conference. The two non-Swedish organizers feei that they express the sentiments of ali participants in thanking J aak Peetre and Hans Wallin as well as the members of the mathematics department at Lund for their warm hospitality. The Editors
CONTENTS. HISTORICAL LECTURE. J.Peetre, Marcel Riesz in Lund. 1 SURVEYS J. Alvarez -M. Milman, Interpolation of tent spaces and applications. 11 M. Cotlar - C. Sadosky, Toeplitz liftings of Hankel forms. 22 R . Fefferman, Some recent developments in Fourier analysis and H" theory on product domains - II. 44 H. G. Feichtinger- K. Grochenig, A unified approach to atomic decompositions via integral group representations . 52 R. Rochberg, The work of Coifman and Semmes on complex interpolation, severa! complex variables, and PDE's. 74 R. Rochberg- A. Tabasco Vignati - M. Vignati- G . Weiss, Interpolation of quasinormed spaces by the complex method. 91 H. Wallin, New and
