Interpolation of linear and non-linear operators and their applications

The report presents various generalizations and refinements of the classical Marcinkiewicz interpolation theorem . The problem of extrapolation of integral operators is considered. An overview is given of the results and their applications related to the method of multiparameter interpolation and to interpolation methods of spaces with a mixed metric. Interpolation theorems are given for a wide class of nonlinear operators covering the Urysohn integral operator.