Interpolation theorems for nonlinear operators in general Morrey-type spaces and their applications (Q828591)

In the paper under review the authors define a much more general class of Morrey-type spaces. They present a number of properties of the new Morrey-type spaces and describe the classes of nonlinear operators under consideration (partially quasi-additive operators) and give examples of operators from these classes, including Urysohn integral operators. They establish general interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. As applications, they obtain analogs of the Marcinkiewicz-Calderón and Stein-Weiss-Peetre interpolation theorems. At last, they prove a quasiweak boundedness criterion for a wide class of Urysohn integral operators.