Goldman, M. L.; Zabreiko, P. P. Kurzweil-Henstock integrability of the product of integrable functions. (Russian. English summary) Zbl 1372.26010 Dokl. Nats. Akad. Nauk Belarusi 60, No. 1, 18-23 (2016). Summary: 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 Hölder condition with the exponent \(\alpha\) or with the module \(\phi\) and a function satisfying the Hölder condition with the exponent \(\beta\) or with the module \(\psi\) such that \(\alpha +\beta> 1\) or \(t^{-2}\phi( t )\psi( t )\) is integrable. Similar results for functions with generalized (Winer, Young, Waterman, Schramm) bounded variations are stated. MSC: 26A39 Denjoy and Perron integrals, other special integrals Keywords:Riemann integral; Lebesgue integral; Kurzweil-Henstock integrals; Riemann-Stieltjes integral; functions of bounded variation; generalized variations of functions PDFBibTeX XMLCite \textit{M. L. Goldman} and \textit{P. P. Zabreiko}, Dokl. Nats. Akad. Nauk Belarusi 60, No. 1, 18--23 (2016; Zbl 1372.26010) Full Text: Link