ScholarLens Back to search
2015•Journal of Inequalities and ApplicationsOpen access

A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality

Rafał M. Łochowski

Open full text 2 citations

Abstract

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.

Open-access reader

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

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.

Key concepts: Riemann–Stieltjes integral, Mathematics, Riemann integral, Daniell integral, Fundamental theorem of calculus, Riemann hypothesis, Inequality, Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality — Research Paper | ScholarLens