ТЕОРЕМЫ ОБ ИНТЕГРИРУЕМОСТИ ПРОИЗВЕДЕНИЙ ФУНКЦИЙ ДЛЯ ИНТЕГРАЛА КУРЦВЕЙЛЯ–ХЕНСТОКА

The article deals with the problem of integrability of the product of integrable functions in the Kurzweil–Henstock sense. The classical theorem states here that the product of an integrable function and a function of bounded variation is also integrable. In the article it is proved that the product of a function with the primitive satisfying the Holder condition with the exponent α or with the module φ and a function satisfying the Holder condition with the exponent β or with the module ψ such that α + β > 1  or t –2 φ( t )ψ( t ) is integrable. Similar results for functions with generalized (Winer, Young, Waterman, Schramm) bounded variations are stated.