Bergh J., Löfström J. Interpolation Spaces. An Introduction

Springer-Verlag, 1976. — X, 207 p.The works of Jaak Peetre constitute the main body of this treatise. Important contributors are also J. L. Lions and A. P. Calderon, not to mention several others. We, the present authors, have thus merely compiled and explained the works of others (with the exception of a few minor contributions of our own). Let us mention the origin of this treatise. A couple of years ago, J. Peetre suggested to the second author, J. Löfström, writing a book on interpolation theory and he most generously put at Löfström's disposal an unfinished manu­ script, covering parts of Chapter 1-3 and 5 of this book. Subsequently, Löfström prepared a first rough, but relatively complete manuscript of lecture notes. This was then partly rewritten and thouroughly revised by the first author, J. Bergh, who also prepared the notes and comment and most of the exercises. Throughout the work, we have had the good fortune of enjoying Jaak Peetre's kind patronage and invaluable counsel. We want to express our deep gratitude to him. Thanks are also due to our colleagues for their support and help. Finally, we are sincerely grateful to Boel Engebrand, Lena Mattsson and Birgit Höglund for their expert typing of our manuscript.Some Classical Theorems.
General Properties of Interpolation Spaces.
The Real Interpolation Method.
The Complex Interpolation Method.
Interpolation of L_p-Spaces.
Interpolation of Sobolev and Besov Spaces.
Applications to Approximation Theory.