The Henstock-Kurzweil approach to Young integrals with integrators in $\BV _\phi $

Abstract: In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral $\int _a^bf\dd g$ exists if $f\in \BV _\phi [a,b]$, $g\in \BV _\psi [a,b]$ and $\sum _{n=1}^\infty \phi ^{-1}({1}/{n})\psi ^{-1} ({1}/{n})<\infty $. In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.

Keywords: Henstock integral, Stieltjes integral, Young integral, $\phi $-variation

Classification (MSC2000): 26A21, 28B15

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