This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Mathematics Low‑priority This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles Low This article has been rated as Low-priority on the project's priority scale.

An L^2 function doesnt even need to have an antiderivative and even even if almost-everywhere-antiderivatives are allowed, they don't need to equal the Volterra integral (not even almost everywhere). Example for both: f(x)=0, for x<1/2, f(x)=1, for x>1/2. I will adjust the article unless someone has objections. Ninjamin ( talk) 17:35, 16 May 2019 (UTC) reply

Some additional properties of the Volterra operator:

• For each ${\displaystyle f}$, ${\displaystyle Vf}$ is Hölder continuous with exponent ${\displaystyle {\frac {1}{2}}}$. Stated and proved in the StackExchange answer linked in the article.
• Using Fubini's theorem one can compute repeated applications of ${\displaystyle V}$ as ${\displaystyle (V^{n}f)(x)=\int _{0}^{x}f(t){\frac {(x-t)^{n-1}}{(n-1)!}}{\text{d}}t}$.

Because I don't have a source (other than lecture notes) on the latter statement, I didn't want to add them to the article. Columbus240 ( talk) 13:29, 12 January 2022 (UTC) reply