Interpolation Theorems for Nonlinear Operators in General Morrey-Type Spaces and Their Applications

We prove new interpolation theorems for a sufficiently wide class of nonlinear operators in Morrey-type spaces. In particular, these theorems apply to Urysohn integral operators. We also obtain analogs of the Marcinkiewicz–Calderón and Stein–Weiss–Peetre interpolation theorems and establish a criterion of $(p,q)$ quasiweak boundedness of the Urysohn operator.