Interpolation Spaces and Allied Topics in Analysis Proceedings of th
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Interpolation Spaces and Allied Topics in Analysis Proceedings of the Conference held in Lund, Sweden, August 29 - September 1,1983
Edited by M. Cwikel and J. Peetre
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editors
Michael Cwike! Technion, Israel Institute of Technology, Department of Mathematics Haifa 32000, Israel Jaak Peetre Lund Institute of Technology, Department of Mathematics S-22007 Lund, Sweden
AMS Subject Classification (1980): 46E30, 46E35, 46M35 ISBN 3-540-13363-1 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13363-1 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
CONTENTS. INTRODUCTORY PAPER. J. Peetre, The theory of interpolation spaces - its origin, prospects for the future.
.
.
TRANSLATION. B. Mityagin,
An interpolation theorem for modular spaces.
10
CONTRIBUTED PAPERS. J. Arazy - S. Fisher, Some aspects of the minimal, Mobius-invariant space of analytic functions on the unit disc.
24
J. Bergh, A non-linear complex interpolation result.
45
W. Connett - A. L. Schwartz,A remark about Calderon's upper s method of 48
interpolation.
M. Cwikel - P. Nilsson, The coincidence of real and complex interpolation 54
methods for couples of weighted Banach lattices. R. De Vore, The K functional for (H1,BMO). E.
. ....
A relation between two interpolation methods.
S. Janson - J. Peetre, Harmonic interpolation.
66 80
92
S. Janson - J. Peetre, Higher order commutators of singular integral operators.
125
1 P. Jones, On interpolation between H and
143
S. Kaijser - J. Wick-Pelletier, Interpolation theory and duality.
152
L. Maligranda, The K-functional for symmetric spaces.
169
C. Merucci, Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces.
183
H. N. Mhaskar, On the smoothness of Fourier transforms.
202
M. Milman, Rearrangements of BMO functions and interpolation.
208
L.-E. Persson, Descriptions of some interpolation spaces in off-diagonal cases.
213
PROBLEM SECTION.
232
THE THEORY OF INTERPOLATION SPACES - ITS ORIGIN. PROSPECTS FOR THE FUTURE Jaak Peetre Matematiska institutionen Box 725 S-220 07 Lund. Sweden
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