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Abstract and Applied Analysis
Volume 1 (1996), Issue 3, Pages 305-325
http://dx.doi.org/10.1155/S1085337596000164

Embedding functions and their role in interpolation theory

Department of Mathematics Technion, Israel Institute of Technology, Haifa 32000, Israel

Received 15 April 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The embedding functions of an intermediate space A into a Banach couple (A0,A1) are defined as its embedding constants into the couples (1αA0,1βA1), α,β>0. Using these functions, we study properties and interrelations of different intermediate spaces, give a new description of all real interpolation spaces, and generalize the concept of weak-type interpolation to any Banach couple to obtain new interpolation theorems.