Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Loéve-Young inequality for the Riemann-Stieltjes integrals driven by irregular signals. Using this result we strengthen some results of Lyons on the existence of solutions of integral equations driven by moderately irregular signals.
CITATION STYLE
Łochowski, R. M. (2015). A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality. Journal of Inequalities and Applications, 2015(1), 1–16. https://doi.org/10.1186/s13660-015-0901-3
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