Аннотация:We consider integrals which play an important role in various fields of harmonic analysis andin some application. Most of these integrals serve to recover a primitive from its derivative which in turn depends on derivate basis and a space where it is defined. We discuss in this talk constructions and descriptive characterizations of the above type of integrals defined on various spaces, in particular on compact groups and related to various derivatives, in particular the derivative defined for functions in L^r-space.