Entropy function spaces and interpolation

We associate to every function space, and to every entropy function E, a scale of spaces Λp,q(E) similar to the classical Lorentz spaces Lp,q . Necessary and sufficient conditions for they to be normed spaces are proved, their role in real interpolation theory is analyzed, and a number of applications to functional and interpolation properties of several variants of Lorentz spaces and entropy spaces are given.  2004 Elsevier Inc. All rights reserved.