A sharp extrapolation theorem for Lorentz spaces

Basing on geometric properties, we give a complete characterization of the Lorentz spaces that can be sharp extrapolation spaces for different types of the behavior of the growth of the norms of an operator in tending to a critical exponent. The results of this article are connected with the calculation of extrapolation constructions in about the same way as theorems of the Calderón–Mityagin type.