arXiv subjects

Henry Riely

Publications and source records attributed to Henry Riely.

2 recordsLinked to original sources

arXiv2022

Characterizing Distances Between Points in the Level Sets of a Class of Continuous Functions on a Closed Interval

Given a continuous function $f:[a,b]\to\mathbb{R}$ such that $f(a)=f(b)$, we investigate the set of distances $|x-y|$ where $f(x)=f(y)$. In particular, we show that the only distances this set must contain are ones which evenly divide $[a,b]$. Additionally, we show that it must contain at least one third of the interval $[0,b-a]$. Lastly, we explore some higher dimensional generalizations.

math.CA↗

arXiv2018

A modification of the Chang-Wilson-Wolff Inequality via the Bellman Function

We describe the Bellman function technique for proving sharp inequalities in harmonic analysis. To provide an example along with historical context, we present how it was originally used by Donald Burkholder to prove $L^p$ boundedness of the $\pm 1$ martingale transform. Finally, with Burkholder's result as a blueprint, we use the Bellman function to prove a new result related to the Chang-Wilson-Wolff Inequality.

math.CA↗