INTERPOLATION THEOREMS FOR THE SPACES $ L_{p,q}$

Abstract

A sharp or optimal interpolation theorem is proved for the Lorentz spaces , generalizing the Marcinkiewicz theorem and refining the Riesz-Thorin theorem and the Stein-Weiss theorem. This theorem extends to the spaces of the real method constructed from any Banach pair; thus it extends also to Besov spaces. Bibliography: 12 titles.