On the integral characterization of some generalized quasiregular mappings and the significance of the conditions of divergence of integrals in the geometric theory of functions

The paper deals with the theory of space mappings. For a generalization of quasiregular mappings important for the investigation of the Sobolev and other known classes of mappings, we propose a simple condition satisfied by all mappings of this kind and only by these mappings. On the basis of conditions of divergence of the integrals, we establish sufficient conditions for the normality of the families of the analyzed classes of mappings and solve the problem of removing isolated singularities. Some applications of the obtained results to mappings from the Sobolev class are discussed.