Interpolation theorems for the spaces $L_{p,q}$

A sharp or optimal interpolation theorem is proved for the Lorentz spaces $L_{p,q}$, generalizing the Marcinkiewicz theorem and refining the Riesz–Thorin theorem and the Stein–Weiss theorem. This theorem extends to the spaces $\overline X_{\theta,p}$ of the real method constructed from any Banach pair; thus it extends also to Besov spaces.
Bibliography: 12 titles.